CRYSTAL PRESSURE OF PHARMACEUTICALS IN NANOSCALE PORES 
 
 
 
 
by 
 
Emily Anne Berglund 
 
 
 
 
 
 
 
A thesis submitted in partial fulfillment 
of the requirements for the degree 
 
 
of 
 
Master of Science 
 
in 
 
Chemical Engineering 
 
 
 
MONTANA STATE UNIVERSITY 
Bozeman, Montana 
 
 
April 2017 
  
  
 
 
 
 
 
 
 
 
©COPYRIGHT 
 
by 
 
Emily Anne Berglund 
 
2017 
 
All Rights Reserved 
ii 
 
ACKNOWLEDGEMENTS 
 
 
I would like to sincerely thank the following people, as my success would not 
have been possible without them.  
I would like to express my gratitude to my advisor, Dr. James Wilking, for his 
unending support, advice, patience and outdated cultural references.  
Additionally, I would like to thank my close friends and family, who survived this 
journey alongside me.  
 
 
 
 
 
 
iii 
 
TABLE OF CONTENTS 
 
 
1. INTRODUCTION .................................................................................................... 1 
 
2. FORMULATION METHOD AND PRELIMINARY DATA ..................................... 7 
 
3. PORE ANALYSIS ..................................................................................................12 
 
4. DIFFERENTIAL SCANNING CALORIMETRY ....................................................25 
 
REFERENCES CITED ...............................................................................................41 
 
APPENDICES ............................................................................................................44 
 
APPENDIX A: Preliminary H-NMR Data ........................................................45 
APPENDIX B: Preliminary Raman Spectroscopy Data .....................................54 
  
iv 
 
LIST OF TABLES 
 
 
Table Page 
 
3.1. Relative Humidity for a Given Saturated Salt Solution ................................14 
 
3.2. Maximum Pore Radius Filled at Given Relative Humidity ..........................16 
 
 
 
 
v 
 
LIST OF FIGURES 
 
 
Figure Page 
 
1.1. Biopharmaceutics Classification System ..................................................... 3 
 
1.2. Photographs of Composite Breakup ............................................................ 5 
 
2.1. Slip-cast Silica Template ............................................................................ 7 
 
2.2. SEM Images of Unimbibed and Imbibed Template .....................................10 
 
3.1. Qualitative Crack Analysis ........................................................................13 
 
3.2. Weight Change of Composites at Different Relative Humidities..................17 
 
3.3. Volumetric Pore Distribution .....................................................................18 
 
3.4. Normalized Pore Distribution ....................................................................19 
 
3.5. Breakup Suppression via Relative Humidity ...............................................20 
 
3.6. Breakup Manipulation via Relative Humidity .............................................23 
 
3.7. Transport Through Composite at 1.0 Relative Humidity .............................23 
 
4.1. Thermogravimetric Analysis of Composite.................................................27 
 
4.2. DSC Curve of Unrestricted Fenofibrate ......................................................28 
 
4.3. DSC Curves of Composites at Different Relative Humidities ......................29 
 
4.4. Crystalline Content of Drug in Composite ..................................................30 
 
4.5. Melting Point Depression ..........................................................................31 
 
4.6. Gibbs-Thomson Calibration Curve .............................................................32 
 
4.7. Modified Gibbs-Thomson Calibration Curve ..............................................33 
 
4.8. DSC Crystal Size Distribution ...................................................................34 
 
 
vi 
 
LIST OF FIGURES — CONTINUED 
 
 
Figure Page 
 
4.9. Crystal Growth with Relative Humidity Increase ........................................35 
 
4.10. Ostwald Ripening of Crystals ...................................................................37 
 
4.11. Ostwald Ripening of Crystals in Composite Geometry ..............................37 
 
4.12. Deformed Crystal Growth ........................................................................39 
 
4.13. Deformed Crystal Growth in Composite Geometry ...................................40 
 
A.1. H-NMR Scans of Crystallizing Unconfined Fenofibrate .............................45 
 
A.2. H-NMR Scans of Crystallizing Fenofibrate in Composite ..........................48 
 
A.3. T2 H-NMR Scans of Composite at 1.0 Relative Humidity ..........................46 
 
A.4. T1T2 H-NMR Scans of Composite at 1.0 Relative Humidity .......................49 
 
B.1. Raman Spectrum of Imbibed and Unimbibed Tablet ..................................54 
 
B.2. Raman Spectrum of Confined and Unconfined Fenofibrate ........................55 
 
B.3. Raman Spectrum of Composites at 0.0 Relative Humidity ..........................57 
 
B.4. Raman Spectrum of Composites at Varying Relative  
        Humidities (VRH) ....................................................................................58 
 
B.5. Raman Spectrum of Composite at 0.0 Relative Humidity vs VRH ..............59 
 
 
  
vii 
 
ABSTRACT 
 
 
Many pharmaceutical compounds are poorly soluble in water. This is problematic 
because most pharmaceuticals are delivered orally and must dissolve in the 
gastrointestinal fluid to be absorbed by the body. Drug dissolution rate is proportional to 
surface area, so a common formulation strategy is to structure drugs as small as possible 
to maximize surface area. A simple approach to create very small particles is to structure 
the compounds within the nanoscale pore space of a colloidal packing. The resulting 
composite undergoes rapid disintegration in water and the exposed drug exhibits 
dramatically improved dissolution rates. We hypothesize that composite breakup is 
driven by the growth of nanoscale crystals, which exert a pressure on the walls of the 
confining pores. To test this hypothesis, we systematically vary the amount of water 
permitted into the composite and use calorimetry to monitor the evolution of the crystal 
size distribution as a function of water content. To exert sufficient pressure to overcome 
the tensile yield stress of the composite, the crystals must be fed by a supersaturated 
phase. Our results suggest that differences in crystal curvature due to crystal confinement 
and crystal size polydispersity generate the necessary supersaturation. These results are 
relevant not just for drug formulations, but for understanding physical processes such as 
salt damage to buildings and road damage due to frost heave.
1 
 
CHAPTER ONE 
 
 
INTRODUCTION 
 
 
Nearly half of the US population have taken a prescription drug in the past 30 days.1 
Oral dosage forms are the most convenient pharmaceutical administration method and are 
thus the most common dosage form.2 When drugs are taken orally, they enter the 
gastrointestinal tract, dissolve in the gastrointestinal fluid and are absorbed through the 
gastrointestinal membrane; thus, two properties, aqueous solubility and intestinal 
permeability dictate the efficacy of oral dosage forms. The efficacy of drug absorption is 
quantified as the fraction of active drug that reaches the circulatory system and is made 
“bioavailable”.3 Intravenous drugs, which are injected straight into the circulatory system, 
have a bioavailability of one. By contrast, the bioavailability of oral drugs is always less 
than one as some active drug is always lost as it passes through the gastrointestinal system. 
Improving the bioavailability of oral dosage forms requires methods of enhancing 
gastrointestinal solubility and permeability. 
Solubility, in this context, refers to the maximum concentration of drug that can 
dissolve in the gastrointestinal fluid.3 Interestingly, it is not equilibrium solubility that 
typically limits bioavailability, but the fact that drugs with poor solubility dissolve very 
slowly. The dissolution rate of a solid is described by the Noyes-Whitney equation, 
Equation 1.1. 
𝑑𝑀
𝑑𝑡
=
𝐷𝐴
ℎ
(𝐶𝑠 − 𝐶𝑥)     (Eqn. 1.1) 
2 
 
Because the dissolution rate, in units of mass per unit time, 
𝑑𝑀
𝑑𝑡
 is directly proportional to 
the difference between the drug saturation concentration, 𝐶𝑠, and drug concentration in the 
bulk solution, 𝐶𝑥, a drug with a low saturation solubility also dissolves very slowly. Here, 
𝐷 is the diffusion coefficient, 𝐴 is the total surface area of the solid form, and h is the 
hydrodynamic layer thickness. The dissolution rate can be increased by reducing the 
hydrodynamic layer thickness through stirring or by increasing the surface area of the drug. 
A faster dissolution rate allows the systemic system more opportunity to absorb the drug 
before excretion, depending on permeability, and is the aim of this study.   
Permeability is related to the extent of absorption and mass transfer rate across the 
human intestinal wall, measured as a fraction of solubilized drug reaching the systemic 
system. A “highly permeable” drug has an absorption rate of at least 90% of the 
administered dose.3 These important parameters inspired the development of a drug 
classification system called the Biopharmaceutics Classification System (BCS), composed 
of four classes shown in Figure 1.1.3 
 
 
 
 
 
3 
 
 
 
Figure 1.1. The Biopharmaceutics Classification System illustrating the four classes of 
drugs dictated by relative permeability and solubility properties.3 
 
 
Drugs with high solubility and high permeability (Class I) are ideal for oral 
delivery, as they achieve the highest bioavailability. These drugs dissolve quickly in the 
gastrointestinal tract and are absorbed well across the intestinal membrane. By contrast, 
Class IV drugs do not dissolve well in the stomach and do not cross the gastrointestinal 
tract effectively. Thus, Class IV drugs have the lowest bioavailability. Drugs that fall into 
the remaining two classifications are also not ideal for oral delivery, and have one efficacy-
limiting property.  Class II pharmaceuticals are drugs that have low solubility, but high 
gastrointestinal permeability. Nearly 1/3 of all drugs fall into this category.4 Altering 
permeability properties of pharmaceutical systems prove much more difficult than 
improving dissolution rates. Due to their popularity and adjustable dissolution rate, as 
depicted by the Noyes-Whitney equation, Class II drugs were chosen as the focus of this 
study.  
4 
 
There are currently several formulation techniques to enhance the dissolution rates 
of low solubility drugs. Different formulation strategies target different properties of drugs 
that greatly contribute to their low solubility. These physiochemical properties range from 
hydrophobicity to crystallinity and pH. Lipid formulations are, arguably, the fastest 
growing interest group of low solubility drug modifications.5 These non-solid oral 
formulations consist of dissolving the drug in hydrophilic or lipophilic surfactants, 
commonly referred to as oral capsules.5  The goal with this strategy is to suspend the drug 
in a dissolved state through the gastrointestinal tract.6 While this technique faces many 
challenges, one of the largest is finding a surfactant that is safe to ingest for encapsulation. 
Commonly used surfactants include docusate sodium and Pluronic-F68.7  
Chemical modifications are also useful for increasing drug solubility, and include 
strategies such as salt formation.7 Salt formation is the most useful technique for solubility 
enhancement of drugs that are very acidic or basic.8 Salt formation strategies utilize the 
knowledge that the conjugate bases and conjugate acids of acidic and basic compounds, 
respectively, have higher solubilities than their counter forms.8 Thus, to achieve higher 
solubilities, the conjugate acid or base of a low solubility drug is precipitated with an 
appropriate counter ion.8 This precipitated salt form has a higher solubility than its non-
salt form. An important consideration with the use of salt formation is the potentially 
harmful effects of drug structure manipulation.7 
Physical modifications, specifically particle size reduction, are among the most 
commonly practiced formulation alteration methods.6 Techniques such as micronization 
have proved effective in increasing solubility. Micronization involves grinding or 
5 
 
pulverizing the drug to reduce the size of drug particle.6 Reducing the particle size increases 
the surface area to volume ratio, thus increasing the contact area of fluid and drug and 
subsequently solubility.9 As previously described, the Noyes-Whitney equation indicates 
an increase in surface area increases the dissolution rate. Thus, particle reduction can allow 
Class II drugs to more closely mimic the ideal bioavailability of Class I drugs.   
A drug particle reduction method is explored here, implementing a porous media  
 
to increase drug surface area. More specifically, this study proposes a tablet production  
 
method in which colloidal silica particles are slip cast, and interstitial spaces are imbibed  
 
with melted drug. When a subclass of Class II drugs, those with a melting temperature  
 
under 120C, are imbibed into a silica template then placed in water, dramatic composite  
 
breakup is observed as shown in Figure 1.2. This dramatic breakup leads to an enhanced  
 
dissolution rate, increasing drug bioavailability. The experimental methods associated with  
 
this formulation approach are outlined in Chapter 2. Understanding the physical  
 
mechanism driving this surprising composite breakup is the focus of the remainder of this  
 
thesis.  
 
 
 
Figure 1.2. Photographs depicting the dramatic break up of a fenofibrate-imbibed colloidal 
silica template (A) immediately after being placed in water and (B) five minutes after being 
placed in water.  
 
 
6 
 
In this study, we find that the loss of mechanical integrity of our composites can be 
attributed to crystal pressure. This is a well-studied phenomenon, and is implicated in 
weather-related damage to road surfaces and monuments.1 Road surfaces are typically 
damaged by the growth of ice crystals and monuments are damaged by the growth of salt 
crystals.1,10 In both cases, if the pressure exerted by a growing crystal exceeds the yield 
strength of the confining pore, breakup can occur. The same mechanism, crystal pressure, 
may be responsible for our low solubility composite breaking. Drug crystals, confined by 
colloidal silica beads, rearrange and grow, exerting a pressure on the walls of the silica. 
When this pressure overcomes the yield strength of the silica, breakup occurs.  
For crystals to grow, they must be in contact with a supersaturated solution, 
composed of a solvent and solute. In our system, the solvent is water and solute is drug. 
So, for a supersaturated solution to exist, water must be able to enter the composite. Chapter 
2 details the formulation method and preliminary data. Chapter 3 describes the use of 
capillary condensation to quantify a network of nanoscale cracks, which allow water to 
enter the composite. Chapter 4 describes the use of differential scanning calorimetry (DSC) 
to follow changes in drug crystallinity and the structural evolution of the crystal size 
distribution as a function of water content in the nanoscale cracks. Appendix A describes 
the use of hydrogen nuclear magnetic resonance (H-NMR) to follow conformational 
changes in the confined drug, and to establish a time-scale for initial crystallization due to 
quenching. Finally, preliminary Raman spectroscopy measurements are discussed in 
Appendix B.  
 
7 
 
CHAPTER TWO 
 
 
FORMULATION METHOD AND PRELIMINARY DATA 
 
 
A formulation method was developed to manufacture composites of colloidal silica 
and drug consistently. To begin, a block of plaster (calcium sulfate hemihydrate) was 
cleaned by scraping the top layer off using a clean razor blade. The block was then rinsed 
in distilled water and left to dry for 24 hours. After the block of gypsum had dried, sterile 
1 mL pipette tips were cut such that they had a desired length of about two centimeters 
with a constant radius. The cut pipette tips, tablet molds, were then placed atop the plaster 
blocks, and 300 uL of colloidal silica suspended in water (Nissan Chemical, MP-1040-H, 
𝑑 = 100nm) was pipetted into the molds. This is a common method of eliminating water 
from a material known as slip casting. The filled molds were left at ambient conditions for 
24 hours, then the tablets were removed by gently lifting the molds from the gypsum, 
depicted below in Figure 2.1. At this point in the process the tablets were a hard, porous 
material.  
 
         
Figure 2.1. The colloidal silica slip casting process. Image A depicts 300 uL of colloidal 
silica contained within molds made from cut 1 mL pipette tips. After 24 hours, the tablet 
was removed from the molds gently, shown in image B.  
 
 
24 hours 
1 cm 1 cm 
8 
 
After the silica tablets were slip cast, drug was melted at a temperature ten degrees 
Celsius higher than its melting temperature. A clean glass microscope slide was placed on 
a hot plate at the desired temperature, here ten degrees Celsius higher than the melting 
point of fenofibrate, 90oC. Pure, powdered fenofibrate (TCI, F0674) was then heaped on 
top of the glass slide. Once the drug was melted, a silica tablet was placed on top. After 
about 30 minutes the color of the composite turned translucent, indicating complete 
imbibition. This indication was possible due the matching refractive indices of the drug 
and silica. Once completely imbibed, the composite was removed from the hot plate via 
tweezers, and was quickly wiped off with a clean tissue. This was done to remove excess 
drug from the outside of the composite. The composite was then placed in a desiccant 
chamber (Drierite) for at least 72 hours, then either tested or moved into a chamber with a 
controlled relative humidity to satisfy a given protocol. Variations of this protocol were 
made, depending on experimental design, but the imbibition process stayed constant 
through all experiments. 
 In Chapter 3, the evolution of microstructure of the composite is analyzed as a 
function of water condensed inside the pores. To analyze them, they were exposed to 
varying relative humidities and weighed. More specifically, once the nine tablets were 
imbibed with fenofibrate, they were placed in a desiccant chamber (0.0 relative humidity, 
Drierite) for three days. They were then weighed on an analytical balance, and weights 
were recorded as the initial weight (in milligrams). After this they were distributed into 
varying relative humidity chambers: 0.0, 0.25, 0.43, 0.75, 0.84, 0.86, 0.90, 0.97, and 1.0.  
The tablets were weighed on an analytical balance every two hours for 10 hours, then about 
9 
 
every four hours for an additional five data points, and finally every 12 hours for two more 
data points. This data was then used to quantify the pore size distribution within the 
composites.  
 In Chapter 4 smaller composites were made by slip casting a smaller volume of 
colloidal silica to reduce their size to fit into DSC sample pans. In this method, only 30 uL 
were pipetted on the gypsum, into cut 200μL pipette tips. Twenty-seven composites were 
manufactured – three for each humidity. After imbibition, they were kept in a relative 
humidity of 0.0. They were contained in the glass vessel with Drierite for three days. They 
were then distributed evenly into nine different relative humidity chambers: 0.0, 0.25, 0.43, 
0.75, 0.84, 0.86, 0.90, 0.97, and 1.0. The composites were enclosed in these chambers for 
three days. This was enough time for the pores to saturate, as demonstrated in the pore 
analysis chapter. After this, the composites were transferred back to the desiccant chamber 
for an additional three days. This was done to drive off residual water, as DSC is a method 
in which the composites are heated and thus are susceptible to data interference from the 
effects of water boiling. Twenty-seven hermetically sealable DSC pans were then weighed 
and recorded. The three composites from each relative humidity were then weighed on an 
analytical balance, and hermetically sealed inside their corresponding pans.  
 A DSC program was constructed in the TA Instruments program designed for the 
specifically for the Discovery Series DSC. Each pan was designated a number 
corresponding with the position they occupied in the autosampler. Every composite was 
exposed to the same regime: a ramp rate of 1oC/min, starting at 35oC and ending at 95oC. 
10 
 
Once a composite was exposed to this, it was removed from the sampling station and the 
system cooled back down to 35oC before beginning the next experiment.  
The main formulation strategy above was initially developed by Dr. James Wilking 
and Dr. Andre Studart at Harvard University. Moreover, at Harvard, several experiments 
were conducted to understand the composition of the silica-fenofibrate system and 
establish trends in breakup. First, micrographs of an unimbibed and imbibed tablet were 
taken using a Scanning Electron Microscope (SEM), shown below in Figure 2.2. This was 
done to gain qualitative insight into the structure of the tablet, and understand the packing 
of the silica beads. The figure below clearly shows void spaces created by the random close 
packing of the silica beads before imbibition (left), and the decrease in void pore space 
after imbibition (right).  
 
 
Figure 2.2. The image on the left is a SEM image of an unimbibed tablet, showing the void 
spaces created by the random close packing of the silica beads. The image on the right is 
of a silica tablet imbibed with fenofibrate, illustrating less available void pore spaces. 
 
 
After gaining a qualitative understanding of the composition of the composite, 
several experiments were conducted to develop breakup constraints. The first was placing 
an unimbibed tablet in water. A tablet of unimbibed silica was placed in water and no 
11 
 
breakup is observed. This suggested the breakup was due to drug interactions with the 
system. The silica tablet was then imbibed with different organic drugs and dropped in 
water. This was tested by Dr. James Wilking at Harvard University, to discern any trend in 
breakup occurrence. The data from this showed only drugs with a melting temperature 
equal to or below 120oC break apart.  To explore this trend further, a drug that was known 
to induce breakup, fenofibrate, was heated above 120oC. The melting point of fenofibrate 
is 80oC, and was usually imbibed at 90oC. This was done to test whether the melting point 
trend was an artifact of the imbibition process instead of the properties of the drug. If the 
fenofibrate composite imbibed at 120oC didn’t break, it would indicate that breakup was a 
result of heating and quenching the tablet. The tablet did, in fact, break up. This suggested 
that the melting point trend observed was due to chemical properties, not the imbibition 
process.  
 
  
12 
 
CHAPTER THREE 
 
 
PORE ANALYSIS 
 
 
For a crystal to exert pressure on the confining walls of a pore space, crystal growth 
must be fed by a supersaturated solution.11 This requires that interconnected cracks must 
exist, which allow water to first enter the composite. Fenofibrate shrinks by about five 
percent in volume when it crystallizes from a liquid to a solid; thus, it is reasonable to 
assume that this shrinkage results in nanoscale cracks and voids. Several experiments were 
designed to test this hypothesis both qualitatively and quantitatively.  
To gain qualitative insight into the possible existence of nanoscale cracks, a 
fenofibrate-silica composite was placed in a shallow dish containing water. A front was 
observed propagating through the composite, exposing cracks in the microstructure, but 
was difficult to see due to the opaque color of the composites and translucence of water. 
Thus, a composite was placed in an aqueous dye solution. The aqueous dye solution was 
only in contact with the bottom of the composite, and thus had to propagate from the bottom 
to the top, where imaging took place. Time lapse images were obtained every few seconds, 
capturing the transport of dye through the composite. After about 30 seconds in the dye, 
no front of dye had reached the top layer of the composite (Fig. 3.1B). After another 50 
seconds, dye was starting to reach the top (Fig. 3.1C). This was followed by dye rapidly 
reaching the top, in a quasi-uniform front (Fig 3.3D, 3.3E, 3.3F). Breakup was seen after 
the front reached the top of the composite. The time lapse showed a network of cracks 
within the composite acting as a transport system for water. Images from this time-lapse 
13 
 
experiment are shown in Figure 3.1. This simple experiment suggested water is, in fact, 
being transported through the composite over time.  
 
 
Figure 3.1. A composite partially submerged in food coloring to observe the transport of 
an aqueous dye solution propagate through a network of cracks (A). After 30 seconds, no 
front of dye is seen on the top of the composite (B). Fifty seconds later, dye makes its first 
appearance on the surface (C). A front of dye then quickly reaches the surface of the 
composite in a matter of seconds, exposing the complex nature of cracks acting as a 
transport system in the composite (D, E, F).  
 
 
To quantify the crack network, several composites were subjected to varying 
relative humidities of 0.0, 0.25, 0.43, 0.75, 0.84, 0.86, 0.90, 0.97, and 1.0 for three days. 
The composites were then weighed while in their respective humidity chambers. Saturated 
salt solutions were made to set varying relative humidities in different chambers, via 
chemical potential (activity) equilibrium.12 Solutions were made from distilled water and 
chemically pure salts, creating slurry mixtures. These mixtures were then placed in glass 
containers and allowed to equilibrate for three days, at ambient temperature. This 
equilibrium vapor pressure of the saturated salt solution at a set temperature, relative to the 
14 
 
vapor pressure associated with water at those same conditions, is known as the relative 
humidity.12 The advantage of using a saturated salt solution, in contrast to a salt solution, 
is that the relative humidity theoretically remains constant even if water enters or leaves 
the chamber. In other words, it is a far more stable system. Since each salt is only able to 
produce one relative humidity at the desired temperature (ambient conditions), eight 
saturated salt solutions were made ranging from about 0.23 to 0.97. To set the relative 
humidity to 0.0, the composites were exposed to a desiccant (Drierite), that depleted the 
system of any moisture. To accomplish a relative humidity of 1.0, pure water was placed 
in a dish alongside the dish of composites. The saturated salt solutions made for this study 
are shown in Table 3.1. 
 
Table 3.1. Measured relative humidities of varying salt solutions used in this experiment.  
Saturated Salt 
Relative Humidity 
(Measured) 
Potassium Acetate 0.225 
Potassium 
Carbonate 
0.432 
Sodium Chloride 0.746 
Potassium Chloride 0.845 
Potassium Chromate 0.865 
Barium Chloride 0.902 
Copper Sulfate 0.973 
 
 
After the relative humidities were set, the experiment proceeded. The only variable 
in the system was the length of time in varying relative humidities. This meant the change 
in weight of the tablet was only due to water condensation in the composite’s nanoscale 
cracks. It is known that water condenses in small pores before large pores. An equilibrium 
15 
 
is reached in different sized pores, dependent on the relative humidity. This relationship 
can be described by the Kelvin-Laplace Equation (Eqn. 3.1),  
 
          (Eqn. 3.1) 
where a is the maximum pore radius that can be filled at a given vapor saturation ratio, γ is 
the liquid/vapor surface tension (73 mJ/m2), θ is the contact angle (0 assuming perfect 
wetting), R is the gas constant (8314.5 mJ/Kmol), T is the temperature (298 K), ?̅?𝐿 is the 
specific volume (0.001 m3/kg), and 𝑝 𝑝0⁄  is the vapor saturation ratio, or relative humidity. 
From this relationship, it was possible to infer a pore radius range for each relative 
humidity. This was accomplished by, first, calculating the maximum pore radius filled for 
a given relative humidity that a composite is exposed to. Because pores fill from small to 
large, it was possible to generate a range of filled pores for each given relative humidity. 
For example, if a composite is exposed to a relative humidity of 0.43, pores with radii 1.26 
nm and smaller will be filled. If a composite is exposed to a relative humidity of 0.75, the 
maximum pore size filled is 3.74 nm. However, we do not know the exact sizes of pores 
within our system. There may not be any pores with a radius of 3.74 nm. Thus, a range of 
possible maximum sizes was established for each given relative humidity. For the example 
of 0.75, water condenses in all pores up to a radius of between 1.26 nm and 3.74 nm. This 
range generation, done for all relative humidities, is shown in Table 3.2.     
 
 
 
 
 
𝑎 =
2𝛾 cos 𝜃
(𝑅𝑇 ?̅?𝐿⁄ )ln (𝑝 𝑝0⁄ )
 
16 
 
Table 3.2. The maximum pore radius filled at a given relative humidity, and the range of 
these pore sizes given varying relative humidities.  
p/po a (nm) 
Range max pore 
size (nm) 
0 0.00  
0.225 0.77 0-0.77 
0.432 1.26 0.71-1.26 
0.753 3.74 1.26-3.74 
0.843 6.23 3.74-6.23 
0.865 7.32 6.23-7.32 
0.903 10.40 7.32-10.40 
0.972 37.38 10.40-37.38 
 
 
A log-log plot of the data collected was generated, shown below in Figure 3.2. The 
plateaus suggest the pores were saturated, and the difference in mass between the plateaus, 
Δm, was used to calculate the change in water volume condensing in pores, since volume 
is proportional to mass. This plot also provided the time needed to saturate the pores at 
varying relative humidities, tc  20 hours. Thus, experiments were planned around exposing 
composites to different relative humidities for at least 48 hours to ensure the pores were 
fully saturated. Additionally, the slope of these lines in the range 0 h ≤ t ≤ 20 h is about 0.5, 
which suggests that the condensation process is diffusion-limited. 
17 
 
 
Figure 3.2. Log-log plot of weight percent increase of the tablet versus time, of imbibed 
tablets kept at different relative humidities over the span of 100 hours. The plateaus suggest 
saturation of the tablets, and the difference between plateaus is indicative of the difference 
of mass changes, Δm. The 1.0 relative humidity composite indicates breakup.  
 
 
The volume changes, proportional to mass changes, associated with different 
relative humidities, along with the pore size range for each relative humidity (Table 3.2) 
are coplotted to illustrate the pore size distribution in the imbibed tablet. This plot is shown 
in Figure 3.3. 
Δm 
0.865 
0.746 
0.432 
0 
0.225 
p/p
0
 
1 
18 
 
 
Figure 3.3. The distribution of pore sizes in an imbibed tablet, using the volume of occupied 
pore space associated with different relative humidities, Δm, and the average of pore range 
associated with each relative humidity. The standard deviation bars illustrate the upper and 
lower limits on the maximum pore size.  
 
 
A large pore will of course contain more water than a small pore; thus, the plot 
above suggests that the distribution is dominated by large pores. To provide a distribution 
that illustrates the number of pores of a given size, the volume change was normalized by 
dividing the mass at each point by the associated radius cubed, ∆𝑚/𝑎3. This generated a 
pore frequency distribution, and is shown below in Figure 3.4., where the large vertical 
standard deviation bars are derived from the uncertainty associated with dividing ∆𝑚 by 
the lower and upper pore range values. The normalized pore size distribution above fits a 
log-normal distribution. Pores with a radius of about one nanometer are most frequent, 
while pores with a large radius of about five nanometers are sparser. Pores between two 
and three nanometers are semifrequent, but it is important to notice the broad range of 
maximum pore size associated with this data point.  
19 
 
 
Figure 3.4. Normalized plot of data shown in Figure 3.3, illustrating the normalized volume 
versus the maximum pore radius. This log-normal distribution shows the frequency of 
pores with a given diameter, a, in a composite. 
 
 
The distribution of pore sizes was important to obtain to analyze the effects relative 
humidity has on a composite. Equilibrium logic implied that imbibed tablets at a lower 
relative humidity have less condensed water in their pores than those at high relative 
humidities. Lower relative humidities have less water available to interact in the 
condensation-evaporation exchange. A lower relative humidity means, by definition, there 
is a lower associated vapor pressure, which implies equilibrium may be obtained faster. 
Interestingly, this is not a phenomenon that is clearly observed. This implies that the 
difference in rate of equilibrium, via condensation, happened faster than the sampling time 
interval.  
This quantitative study successfully demonstrates the existence of nanoscale cracks 
in the composite that permit water to enter the composite. The implication of water within 
the composite supports the hypothesis of the generation of a supersaturated solution 
allowing for the growth of crystals.  
20 
 
After the quantification of nanoscale cracks in composites, new composites were 
subjected to the previous protocol. After 72 hours of exposure to varying relative 
humidities, the composites were dropped in water and breakup was recorded. This was 
done to detect any qualitative impact exposing composites to different relative humidities 
has on breakup intensity.  It was observed that breakup became drastically less dramatic as 
imbibed tablets were subjected to higher relative humidities. The last image, a composite 
held at a relative humidity of 0.97, shows a large crack. This crack existed before the 
composite was dropped in the water. In other words, dropping this composite in water did 
not have any effect on the mechanical integrity. The difference in breakup intensity is 
shown in Figure 3.5.  
 
 
Figure 3.5. Images taken five minutes after imbibed tablets, at different relative humidities 
for three days, were placed in water. Images are in order of increasing relative humidity 
left to right, by row: 0.225, 0.432, 0.746, 0.865, 0.902, 0.973.  
 
 
The decrease in breakup intensity shown in Figure 3.5 may be because as relative 
humidity is increased, more void pore space is occupied by condensation. At low relative 
humidities, large pores remain water vacant, since pores fill small to large. When these 
21 
 
composites are then placed in water, the medium and large pores fill with water, mobilizing 
drug and create a supersaturated solution. This supersaturated solution drives crystal 
growth, and the pressure exerted by the crystals on the silica causes breakup. There are less 
vacancies in composites exposed to higher relative humidities. This means that more pore 
sizes have been filled with water due to condensation, and have thus generated a 
supersaturated solution and generated crystal growth. This growth may be enough to break 
the composite apart, as seen in the case of a composite at a relative humidity of 0.973. 
When the sparse, as seen in Figure 3.4, large pores fill with water when dropped in water, 
they too generate a supersaturated solution. However, due to their infrequency in the 
system, do not collectively generate enough pressure via crystal growth to exceed the yield 
strength of the silica. This coincides with the idea that generating a supersaturated solution 
in the largest pores may not generate a pressure large enough to break the composite.  
To explore this hypothesis, an experiment was developed around exposing a 
composite to a relative humidity of 1.0. If the previous hypothesis is correct, crystals will 
grow when the composite is placed in a humidity of 1.0 and crack the composite. When 
placed in water, there should be no growth as all pores are filled with grown crystals and 
water. When some of the water in the pores is driven off due to a pressure change induced 
by exposed the composite back to a relative humidity of 0.0, there should be minimal 
breakup in water. Additionally, when exposed to a relative humidity of 1.0, the pores should 
fill completely and thus no longer act as a water transport system. 
A composite was exposed to a relative humidity of 0.0 for 24 hours and placed in 
water. Breakup is observed. A composite is then placed in a relative humidity of 0.0 for 24 
22 
 
hours then 1.0 for 24 hours, and finally placed in water. This is enough time (as shown in 
Figure 3.2) to saturate the pores within the composite. This saturation induces a 
supersaturated solution and crystals grow, cracking the composite. When the composite, 
with filled pores, is placed in water there is no longer a transport network and water cannot 
enter the composite. Thus, crystal growth doesn’t occur as a result of being placed in water. 
If we take a new composite and expose it to the same regimen as the previous one, but 
place it back in a relative humidity of 0.0 for 24 hours before dropping it in water, we drive 
off some of the water in the pores. The change in relative humidity causes a pressure change 
and water evaporates from the pores. However, crystals have already grown because of the 
supersaturated solution generated when placed in a relative humidity of 1.0. Thus, when 
placed in a dish of water, only minimal crystal growth happens. That is, the water reenters 
the vacant large pores and generates another supersaturated solution, but the crystals are 
less inclined to grow, as they have already grown in a way to reduce their surface energy 
(the driving thermodynamic force for crystal growth as discussed extensively in the 
following chapter). This means only minor crystal growth is occurring, which is reflected 
in the minimal breakup, or swelling, of the composite in water.  Experimental results from 
this experiment are shown in Figure 3.6.   
 
 
23 
 
 
Figure 3.6. Imbibed tablets subjected to 0.0 and 1.0 relative humidities for 24 hours at a 
time, then dropped in water. All images were taken five minutes after the tablets were 
placed in the water. 
 
 
To test the hypothesis that water does not transport through a composite held at a 
relative humidity of 1.0, a composite was subjected to the previous protocol and placed in 
food coloring diluted 1:2. Another composite was subjected to a relative humidity of 0.0 
for 24 hours, then placed in food coloring diluted 1:2 as a control. The result from the 
experiment is shown in Figure 3.7, illustrating that water does not appear to transport 
through a composite kept at relative humidity of 1.0 failing to disprove our hypothesis.  
 
 
Figure 3.7. A composite placed in a relative humidity of 0.0 for 24 hours, 1.0 for 24 hours, 
then into a 1:2 solution of food coloring and water, shown on the left. A composite placed 
in a relative humidity of 0.0 for 24 hours then into a 1:2 solution of food coloring and water 
is shown on the right.  Both images are taken five minutes after being placed in the 1:2 
solution of red food coloring and distilled water, and illustrate the lack of solution 
transported through the composite held at a relative humidity of 1.0.  
 
 
Studying the microstructure of nanoscale cracks in the composite results in the 
conclusion that they act as a transport system for water through the composite. This 
24 
 
quantification of nanoscale cracks supports the hypothesis that a supersaturated solution 
may exist in the composite, composed of water and drug. To understand the impact that 
this supersaturated solution has on crystal growth in the composite, Differential Scanning 
Calorimetry (DSC) is conducted.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
25 
 
CHAPTER FOUR 
 
 
DIFFERENTIAL SCANNING CALORIMETRY 
 
 
Differential scanning calorimetry (DSC) measurements were performed on drug-
silica composites to quantify two parameters: (1) the fraction of crystal drug content and 
(2) the drug crystal size distribution. DSC is a thermoanalytical method that measures the 
heat necessary to raise the temperature of a sample, as a function of temperature.13 This 
technique can measure many characteristics of a sample such as heat capacity, glass 
transition, as well as the temperature and latent heat associated with a phase transition.13 
The heat capacity of a sample is given by the slope of the generated plot, heat flow versus 
temperature.13  Phase transitions are indicated by the relative difference in heat flow needed 
to keep the temperature of a sample and reference equal. For example, when a sample 
undergoes an exothermic process such as crystallization, less heat is required to raise the 
sample temperature than the reference. Likewise, when a sample undergoes an endothermic 
process such as melting, it absorbs heat, and the system must increase the heat flow to the 
sample pan to keep the temperature of the sample and reference pans equal.  
Measuring the temperature and latent heat associated with the melting of drug in 
our composite was critical for determining the phenomenon responsible for composite 
breakup. The drug is solid at room temperature, so when heat is applied we expect it to 
melt. The area under the concave, endothermic, DSC curve allowed us to calculate the 
amount of crystalline drug in the composite. Changes in melting temperature provide 
26 
 
insight to the size of the crystal confined by the pores, as larger crystals melt at higher 
temperatures.  
To calculate the crystal and amorphous content of drug in the composite, two 
parameters must be known: (1) the enthalpy of melting (heat of fusion) for a pure 
crystalline sample Hm, pure, and (2) the mass fraction of the sample occupied by the organic 
drug, mc. With this information, as well as the enthalpy associated with the sample of 
interest Hm, sample, it was possible to calculate the fraction of crystalline drug c in a given 
sample using the following equation.  
                                                 𝜑𝑐 =  
∆𝐻𝑚,𝑠𝑎𝑚𝑝𝑙𝑒
𝑚𝑐∆𝐻𝑚,𝑝𝑢𝑟𝑒 
        (Eqn 4.1) 
To determine mc, thermogravimetric analysis (TGA) is used. TGA uses a highly 
sensitive scale to monitor the mass of the composite as a function of temperature. At 
temperatures above 150C, the organic drug in the tablet begins to oxidize and degrade and 
will be released as carbon dioxide and oxygen; by contrast, the inorganic silica does not 
degrade at these temperatures. Thus, the corresponding decrease in mass can be used to 
determine the mass fraction of drug in the original sample. A representative measurement 
is shown below in Fig. 4.1 for a fenofibrate-silica composite, providing mc = 0.182.  
27 
 
 
Figure 4.1. Thermogravimetric analysis (TGA) plot of mass as a function of temperature 
for a fenofibrate-silica composite heated to 500oC at a ramp rate of 3oC/min. The 
fenofibrate occupies about 18% of the tablet by weight.  
 
 
To determine Hm, pure for fenofibrate, as well as to establish a benchmark, DSC 
measurements were performed on pure fenofibrate powder. DSC measurements were 
performed on three independent samples. For each measurement, a sample of known mass 
was placed in a hermetically sealed pan alongside an empty reference pan. Each pan was 
placed on a pedestal that records the amount of energy required to keep both the reference 
and sample pan at the same temperature. All DSC runs were conducted with a heat ramp 
rate of 1oC/minute, starting at ambient temperature. A representative DSC measurement is 
shown in Fig. 4.2. The melting point, Tm of the pure drug was measured to be 80.2 ± 0.05
oC, 
with Hm, pure = 31.52 ± 0.37 kJ/mol. These results are consistent with the published values 
of Tm = 80.5
oC and Hm, pure = 32.4 kJ/mol, with percent differences of about 0.37% and 
2.75%, respectively.14   
28 
 
 
Figure 4.2. Differential scanning calorimetry (DSC) plot of relative heat flux Q as a 
function of temperature T for pure fenofibrate, heated at a rate of 1oC/min. The plot is the 
average of three runs and the standard deviation is smaller than the symbol size. These 
results yielded an average melting temperature of Tm = 80.2 ± 0.05
oC and average heat of 
fusion of Hm, pure = 31.52 ± 0.37 kJ/mol. 
 
 
To determine the crystalline content of drug in the composite and the drug crystal 
size distribution, both as a function of relative humidity, samples were prepared as 
described in Chapter 2. Following imbibition, samples were immediately transferred to a 
low humidity chamber (p/p0 = 0) for 24 hours. After 24 hours, the composites were 
transferred to different relative humidities of 0.0, 0.25, 0.43, 0.75, 0.84, 0.86, 0.90, 0.97, 
and 1.0 for three days. They were removed from the respective relative humidity chambers 
and moved back into the low humidity chamber for an additional three days to drive off 
the water that condensed in the pores during residency in humidity chambers. This was 
done as the presence of water would adversely affect the DSC results. It was assumed that 
changes resulting from the condensation of water are permanent and unaffected by the 
removal of the condensed water prior to the DSC measurements. To perform DSC 
29 
 
measurements, samples were meticulously weighed and sealed in hermetic DSC pans. 
Samples were then transferred into the DSC. A program was constructed in TRIOS to 
dictate the experimental protocol. All samples were run starting at a temperature no higher 
than 35oC, with a ramp rate of 1oC/minute up to 95oC. Results from this experiment are 
shown in Fig. 4.3. 
 
 
Figure 4.3. Differential scanning calorimetry (DSC) results of imbibed tablets that were 
subjected to different relative humidities, p/p0 for three days. Two aspects of the data 
should be noted: (1) the integrated areas associated with these curves are proportional to 
the fraction of drug in crystal form, and (2) the melting point depression can provide crystal 
size. Data plots are offset for clarity. 
 
 
To calculate the crystalline content of drug in the composite from the DSC curves 
in Fig. 4.3, the integrated area associated with each curve are measured with the TRIOS 
software and Equation 4.1 was used to calculate the fraction of crystalline content in the 
composite as a function of relative humidity. Surprisingly, there were minimal changes in 
p/p
0
 
0.22 
0.43 
0.74 
0.84 
0.90 
0.97 
30 
 
the percent crystallinity with varying relative humidity, as shown in Fig. 4.4. This 
suggested that the overall amount of drug crystallized in each tablet did not change 
significantly with the condensation of increasing amounts of water, leading even to 
breakup. Thus, our hypothesis of amorphous drug feeding the crystal growth of crystalline 
drug was not supported by the DSC results. 
 
 
Figure 4.4. Mass fraction of drug in crystal form c calculated for each tablet kept in 
varying relative humidities, p/p0. Three trials are conducted, and the mean is shown here 
with standard deviations smaller than the symbol size. This figure shows that percent 
crystallinity does not change with the induction of water into the composite.  
 
 
To determine the evolution of the crystal size distribution with p/p0 the Gibbs-
Thomson equation was used. The Gibbs-Thomson equation which follows states that 
melting point depression Δ𝑇 is inversely proportional to crystal size, where d is the 
diameter of the crystal.  
𝛥𝑇 =  
  4𝜆𝑠𝑙𝑇𝑚,𝑏
∆𝐻𝜌𝑑
       (Eqn 4.2) 
31 
 
Here, 𝜆𝑠𝑙 is the interfacial tension, 𝑇𝑚,𝑏 is the melting temperature of large drug crystals, 
∆𝐻 is the heat of fusion of the crystalline drug, and 𝜌 is the drug density. To highlight this 
melting point depression effect, DSC runs of the composite and large fenofibrate crystals 
are plotted in Fig. 4.5. 
 
 
Figure 4.5. The melting point depression, Δ𝑇, as used in the Gibbs-Thomson equation. This 
melting point depression refers to the difference between the melting point of large 
(macroscale) fenofibrate crystals and our composite samples. Data plots are offset for 
clarity. 
 
 
To utilize the Gibbs-Thomson equation, the most straightforward approach was to 
systematically vary drug crystal size and construct a calibration plot. To do this, we used 
templating silica spheres of varied sizes to construct porous media with different sized 
pores. It has been demonstrated mathematically that the maximum sized sphere that can fit 
in a two-dimensional pore formed by three “kissing spheres” is approximately 15% of the 
diameter of the larger spheres. For example, the maximum size sphere that can fit into a 
pore formed by colloidal silica with D = 100 nm is 15 nm. However, based on TEM images 
32 
 
taken at Harvard University by Esther Amstad, the average crystal size in a porous material 
composed of colloidal silica with D = 100 nm is 9 nm. Thus, the calibration curve was 
constructed using the following relationship.  
𝑑 = 0.09𝐷                                   (Eqn. 4.3) 
Fenofibrate-silica composites were made using four varied sizes of colloidal silica,  
 
DSC measurements were performed on each, and the melting point depression Δ𝑇 was  
 
measured for each and plotted against the inverse maximum diameter of crystal d based on  
 
Equation 4.3. The resulting plot, fit with a straight line is shown in Figure 4.6.  
 
 
 
Figure 4.6. Melting point depression Δ𝑇 as a function of the inverse of crystal size, d. Data 
was extracted from DSC measurements on fenofibrate-silica composites made using four 
different sizes of colloidal silica and the crystal size based on the relationship: d = 0.09D.  
 
 
To plot the calibration curve in an alternative manner, the melting point of the 
crystals in the composite was plotted as a function of the inverse of the crystal size, d as 
shown in Fig. 4.7. 
 
33 
 
 
Figure 4.7. An adjusted calibration curve of the melting point of crystals see in DSC plots 
as minima, and maximum diameter of crystal confined in a pore provided by silica beads.  
 
 
The calibration curve was then used to convert each DSC plot to a crystal size 
distribution. Each melting temperature is directly related to the diameter of crystal, so the 
x-axis was directly converted from temperature to crystal diameter. In addition, heat flux 
is directly proportional to the mass of crystals at a given size; so, by simply multiplying Q 
by -1, the y-axis was converted into arbitrary units of intensity. This provides the evolution 
of the crystal size distribution with respect to relative humidity. We observed several 
striking phenomena. At low humidities, the crystal size distribution is peaked around a 
single crystal size (d  8) with a slight shoulder (d  11). As the composites were exposed 
to greater humidities, the shoulder grew into a clear peak and shifts to larger size. This is 
plotted in Fig. 4.8. 
34 
 
 
Figure 4.8. DSC data from Fig. 4.5 after conversion to a crystal size distribution. Each 
curve represents the mean of three DSC runs. Deviation in the data is less than the symbol 
size. Data plots are offset for clarity. 
 
 
To more clearly understand the evolution of crystal size with relative humidity, we 
plot the primary peaks in the size distribution with respect to relative humidity. This data 
is shown in Fig. 4.9. where the left-most peak is represented with red symbols, and the 
right-most peak is represented with blue symbols. The data implied that the composite 
breaks when placed in a relative humidity above 0.93. This agreed with observations made 
during the experiment and suggests that a redistribution of crystal sizes could be the driving 
force for breakup. 
0.22 
0.43 
0.74 
0.84 
0.90 
0.97 
p/p
0
 
35 
 
 
Figure 4.9. Plot of the primary peak position as a function of relative humidity. It shows 
that the crystal size increases with the induction of more water. The dashed line represents 
a threshold: the maximum size of a spherical crystal that could fit in a pore provided by 
silica beads with D = 100 nm. When the crystal grows larger than the pore size, breakup is 
expected.  
 
 
The DSC data shows that larger crystals are growing at the expense of smaller 
crystals. This phenomenon is known as Ostwald ripening and is typically associated with 
coarsening behavior in emulsions and other colloidal systems; however, this phenomenon 
could also generate the supersaturation necessary for crystal pressure and drive composite 
breakup.15  
To understand how Ostwald ripening could create a supersaturation, consider two 
nanoscale crystals: one slightly larger than the other (Fig. 4.10a). Initially, the crystals are 
dry, and are then immersed in water (Fig. 4.10b). Based on equilibrium thermodynamics, 
when the crystals come in contact with water, they dissolve until they reach equilibrium 
36 
 
saturation. The saturation solubility of nanoscale crystals is described by the Ostwald-
Freundlich equation, which relates the equilibrium saturation solubility associated with a 
particle, Cr to the radius of the particle, r. 
𝜌
𝑅𝑇
𝑀
𝑙𝑛
𝐶𝑟
𝐶∞
=
2𝛾
𝑟
   (Eqn. 4.4) 
Here, 𝜌 is the drug density, 𝑅 is the gas constant, 𝑇 is temperature, 𝑀 is molar mass, 𝐶𝑟 is 
the solubility of a particle with radius of curvature 𝑟, 𝐶∞ is the solubility of a particle with 
a very large radius of curvature, and 𝛾 is the interfacial surface tension. From this 
relationship, it is clear the smaller the crystal, the greater the equilibrium saturation 
solubility (𝐶𝑠𝑎𝑡,𝑆 > 𝐶𝑠𝑎𝑡,𝐿). This means that as both crystals continue to dissolve, the larger 
crystal will reach equilibrium saturation before the smaller crystal. Meanwhile, the smaller 
crystal will continue to dissolve as long as 𝐶𝑑𝑟𝑢𝑔 < 𝐶𝑠𝑎𝑡,𝑆. As a result, the solution will 
become supersaturated with respect to the large crystal (𝐶𝑑𝑟𝑢𝑔 > 𝐶𝑠𝑎𝑡,𝐿).  If the scenario 
depicted in Fig. 4.10a-e occurs within the confines of a pore, the supersaturation generated 
by the smaller crystal could provide the conditions necessary for the larger crystal to exert 
a pressure on the pore walls, as shown by the series of illustrations in Fig. 4.11.  
 
 
 
 
 
37 
 
 
Figure 4.10. (a) Ostwald ripening of crystals in water. Consider two nanoscale crystals: 
one large, L and one small, S. (B) When the pore is filled with pure water, the concentration 
of drug in the water will be less than the solubility of both the large and small crystals. (C) 
As both crystals dissolve, the larger crystal will reach equilibrium saturation before the 
smaller crystal. The continued dissolution of the smaller crystal will generate a 
supersaturated solution with respect to the large crystal and will drive growth of the larger 
crystal (D, E).  
 
 
Figure 4.11. Ostwald ripening of crystals within a pore provided by silica spheres. (A) 
Heterogenous crystallization of fenofibrate would likely lead to a distribution of crystal 
sizes in the composite. (B) Once the pores are filled with water, the Ostwald ripening 
phenomenon described in Fig 4.10 could result in a pressure being exerted on the walls of 
the pore (C, D).  
 
A B C 
D E 
38 
 
In the same manner, crystal pressure could also be generated by the growth of 
deformed crystals.16 For example, consider a cylindrical crystal with two spherical ends, 
confined by a cylindrical pore (Fig. 4.12A). The spherical caps have a greater mean 
curvature than the central cylindrical portion of the crystal; thus, according to the Ostwald-
Freundlich equation, the caps will have a higher saturation solubility than the cylindrical 
center (𝐶𝑠𝑎𝑡,𝑐𝑎𝑝𝑠 > 𝐶𝑠𝑎𝑡,𝑐𝑒𝑛𝑡𝑒𝑟). This means that if the crystal is immersed in water, the 
central region will reach equilibrium saturation before the spherical caps. However, the 
caps will continue to dissolve as long as 𝐶𝑠𝑎𝑡,𝑐𝑎𝑝𝑠 < 𝐶𝑑𝑟𝑢𝑔.  As a result, the solution will 
become supersaturated with respect to the cylindrical region of the crystal (𝐶𝑑𝑟𝑢𝑔 >
𝐶𝑠𝑎𝑡,𝑐𝑒𝑛𝑡𝑒𝑟).  If the scenario depicted in Fig. 4.12a-e occurs within the confines of a pore, 
the supersaturation generated by the deformed crystal could provide the conditions 
necessary for the larger crystal to exert a pressure on the pore walls, as shown by the series 
of illustrations in Fig. 4.13. Due to the non-spherical nature of the pores in the composites, 
it is very likely that deformed crystals are indeed forming in the pores.   
39 
 
 
Figure 4.12. A deformed crystal redistributing its mass to minimize surface energy, leading 
to pore breakup. A deformed crystal exists in a non-spherical pore (A). Due to the 
difference in radii of the planar edges and spherical caps, the solubility of the edges is less 
than the caps (B, C). The caps dissolve until they are in equilibrium with surrounding 
solution (D, E). Because the concentration of drug in the solution is greater than the 
solubility of the planar edge, it is a supersaturated solution (D, E). This leads to the growth 
of the planar edges at the expense of the spherical caps (F).  
 
 
 
 
 
A 
B 
C D 
E F 
40 
 
 
Figure 4.13. A deformed crystal in the pore space provided by the colloidal silica 
redistributes its mass to minimize surface area, and thus surface energy (A). The spherical 
caps, with a smaller radius of curvature thus larger solubility, dissolve in water more than 
the planar regions (B). The planar region is then in a supersaturated solution as the 
concentration of drug in the water exceeds the solubility of the flat surface, and grows 
outward (C). The growth of the planar regions on the walls of the silica applies a pressure 
that eventually overcomes the yeild strength of the composite, due to growth exceeding the 
size of pore (D).  
 
 
It is entirely possible that both Ostwald ripening and rearrangement of deformed 
crystals are happening simultaneously within pores. The DSC data implies there are at least 
two definite crystal sizes present in the pores, but there are likely many more. This is 
suggested by the slow decent into the melting point of a confined drug, easily seen when 
compared to the sharp melting point peak in the unconfined drug curve. Multiple crystals 
could be simultaneously rearranging to minimize their surface energy, while also playing 
a role in multi-crystal Ostwald ripening. This dynamic and complex system may be 
responsible for the ultimate failure of the mechanical integrity of the composite.  
 
 
 
 
 
 
41 
 
 
 
 
 
 
 
APPENDICES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
42 
 
 
 
 
 
 
 
APPENDIX A 
 
PRELIMINARY H-NMR DATA 
43 
 
Proton Nuclear Magnetic Resonance (H-NMR) was used to analyze crystallization 
mechanics, with respect to relative humidity changes, over time. All scans and data 
construction were done by Linn Thrane, a Ph.D. candidate working in the lab of Dr. Joseph 
Seymour at Montana State University. Data analysis was done in collaboration with Linn 
Thrane, Dr. Seymour, and Dr. Wilking. H-NMR was conducted for pure drug, not imbibed 
in a tablet, to understand if the local physical and chemical environment changes when 
compared to drug confined in the pores of a tablet. The composites used in this study were 
made from colloidal silica (SiO2) imbibed with fenofibrate (C20H21ClO4). Composites were 
tested after water (H2O) condenses inside void pore space of the composite. It is obvious 
from the molecular formulas that the only entities measured using H-NMR were the drug 
and water in the pores, as H-NMR measures hydrogen nuclei in molecules.  
T1 and T2 relaxation times were obtained for the restricted and unrestricted drug. 
Two plots were generated: a probability plot of T2 relaxation times, as well as a log-log 
plot of T1 versus T2 relaxation times. A T2 probability versus log T2 plot lead to deductions 
about drug mobility in pores, as well as relative quantities of chemical entities within the 
tablet. Once in the magnet, every individual molecular spin experiences a different 
magnetic field. This is a consequence of intermolecular interactions; that is, the 
neighboring influences lead to an eventual dephasing of spins. This dephasing leads to a 
signal reduction over time, or T2 relaxation time.
17 Molecules confined in pores interact 
with and influenced neighboring molecular spins more than less restricted molecules. This 
increased interaction leads to longer T2 relaxation times. Drug that is in an amorphous state 
has more mobility than its crystal counter structure, and thus a longer T2 time is expected. 
44 
 
Additionally, pure unimbibed drug is expected to have a longer T2 time than imbibed drug, 
due to pore restriction.  
The T1T2 plots served to verify the experimental method, track molecular 
arrangements of populations within the tablet, and indicated whether the sample was more 
or less solid-like. When a magnetic field is applied to the sample, the molecules are forced 
into a perpendicular orientation (from the z—axis to the x—axis). T1 relaxation times are a 
measure of how long it takes for the molecules to reorient into the z-axis after the 
magnetization is removed.17 When analyzed alongside T2 relaxation times, information 
about the physical state of the sample was revealed. A short T2 time along with a long T1 
time indicated a more solid-like substance, while a long T2 and T1 time implied a more 
liquid-like substance. This information was used to gather data about the conversion of a 
more liquid-like amorphous drug to a more solid-like, or crystalline, structure.  
To understand the timescale of crystallization of drug in the pores because of 
imbibition, pure drug was melted in an NMR tube then placed in the magnetic and 
measured. Specifically, a 5 mm NMR tube (Wilmad Economy) was filled with pure 
fenofibrate, straight from the bottle received from TCI. After being filled to 90% capacity, 
the tube was placed in an oven at 90 oC until melted. The tube was then quickly capped 
and transferred into the magnetic, when the analysis begun. Measurements were taken 
every three minutes at ambient conditions. This interval was chosen to maximize data 
collected while minimizing noise via multiple scans per data point. Data from this 
experiment is shown in Figure A.1.  
45 
 
 
Figure A.1. T2 H-NMR scans of pure fenofibrate recrystallizing after being melted. This 
illustrates the time scale of crystallization of the drug, as well as conformational changes 
from primarily amorphous to primarily crystalline content.  
 
 
Figure A.1 shows equilibrium was acquired, due to the lack of signal variance, after 
about 21 minutes after melting. This illustrated the evolution from being completely 
amorphous to mostly crystalline. The longer T2 time of the right-most peak implied a more 
mobile population, indicative of amorphous content. Contrarily, the shorter T2 time of the 
left-most peak implied a less mobile population, indicative of crystalline content. The peak 
with the longer T2 diminishes over time, while the other peak seems to increase in intensity. 
This observation implies a growing crystalline population and shrinking amorphous 
population. Due to the conservation of mass, it is logical to assume that the amorphous 
content evolved into crystals as a function of time. This supports our hypothesis of drug 
crystallization post imbibement.  
To explore this hypothesis further, an analysis of crystallization over time was 
conducted on drug in a tablet. Three silica templates, all slip casted in the way previously 
described, were cut into pieces small enough to fit into an NMR sample tube. Once 
46 
 
fenofibrate was melted on a hot plate at 90oC, the silica template fragments were placed on 
top. After the pieces turned clear, indicating imbibition was complete, the pieces were 
taken off the hot plate and wiped clean with a tissue. The clean pieces of tablet were 
transferred into a NMR sample tube and loaded into the magnet promptly. Scans were 
initiated immediately.  Scans of the evolving tablet pieces were taken every 15 minutes 
until there was no variation in the T2 relaxation times and intensities, about 27 minutes. 
Results from this experiment are shown as follows in Figure A.2. 
 
 
Figure A.2. T2 H-NMR scans of drug recrystallizing inside the porous silica, immediately 
after imbibition. This plot shows the evolution of amorphous to crystalline drug, within a 
time scale of two and a half hours. 
 
 
Figure A.2. clearly illustrates the evolution of amorphous to crystalline drug, like 
the previous figure. It is evident from this data that drug crystallization happens over, about, 
two and a half hours. As expected, crystallization happened more slowly when confined in 
pores than when unconfined as in the previous plot. The intensity of the two peaks equalize, 
implying an equilibrium state of amorphous and crystalline content. Similar to the pure, 
47 
 
powder drug previously, it is hypothesized that the amorphous content is evolving into 
crystals inside the silica pores.  
Many experiments conducted in this study examined the effects of relative humidity 
on molecular structure of the drug within the silica pores. In an effort to explore the 
hypothesis that water condensation was inducing a structural evolution of the drug, H-
NMR scans of an imbibed tablet subjected to 100% relative humidity were taken. 
Specifically, fenofibrate was melted at 90.1oC on a glass plate atop a hot plate. A silica 
template made as previously described was placed on top of the melted drug, until the tablet 
was clear indicating complete imbibition. The imbibed tablet was removed from the melted 
drug, wiped off with a tissue, and placed in 0% relative humidity for three days. The tablet 
was then removed and cut into pieces small enough to fit in the sample tube. This was done 
with four sample tubes. Once loaded in the tubes, the tablets were moved to a glass chamber 
held at 100% relative humidity. After the H-NMR was calibrated and ready to generate T2 
and T1T2 plots, the appropriate sample tube was capped and placed in the magnet. Scans 
of the tablet were done after one, three, 7, and 14 days. T2 plots from these samples are 
shown in Figure A.3.  
 
 
 
 
 
48 
 
 
Figure A.3. H-NMR T2 relaxation time scans of an imbibed tablet held at 100% relative 
humidity for one, three, seven and 14 days, showing the evolution of drug structure 
confined in pores. As time increases, water content increases and the two drug structures 
change conformation implying more restriction.  
 
 
There are several obvious differences in the plots shown in Figure A.3. The first is 
the evolution of a third peak within the first three days. This implies three different 
populations within the pores of the silica. This may illustrate the condensation of water in 
the pores over time. The peak with the longest T2 relaxation time was indicative of water, 
as that was the most mobile species in the tablets. The other two peaks are indicative of the 
drug structure. The peak with the shortest T2 time indicated a more solid-like structure, 
possibly crystallized drug, while the longer T2 time indicated a more liquid-like structure, 
possibly amorphous drug. When compared to the relaxation times of the previous figure 
showing the hypothesized evolution of amorphous drug to crystalline, the two left-most 
49 
 
peaks illustrate similar changes. It may also be true the shortest T2 time indicated a pore 
containing a larger, more restricted crystal, while the longer T2 time suggested a pore 
containing small, less restricted, crystals. If the latter was true, it would be supportive of 
the hypothesis of Oswald Ripening in the pores. The plots would indicate an evolution 
from smaller, less restricted crystals, to large, more restricted crystals, until an equilibrium 
was reached. It should also be noted that the analysis of the two smaller peaks becomes 
more difficult as the time scale is increased, due to the dwarfing effect of the increasing 
water peak intensity. To understand this evolution from amorphous to crystalline drug more 
clearly, T1T2 plots were generated as shown in Figure A.4. 
 
 
Figure A.4. T1T2 H-NMR scans of imbibed tablets kept at 100% relative humidity for (from 
left to right) one, three, 7, and 14 days. The changes in population distribution implies 
changes to the drug structure, with the water peak increasing in intensity as well as T1 and 
T2 times.  
 
 
50 
 
The first peak labeled above experiences decreased T1 and T2 times with respect to 
increased time in 100% relative humidity. These relaxation times indicate an evolution of 
a more solid-like substance. This agrees with the data in the previous figure, implying 
either amorphous drug is evolving into crystalline drug, or smaller crystals are becoming 
larger, more restricted crystals over time. 
The second peak labeled in the plots above is representative of water within the 
pores. As time increases, the water peak increases in intensity as well as T1 and T2 
relaxation times. This implies an increase in water content within the pores. This makes 
sense as the longer the imbibed tablet was in the 100% relative humidity chamber, the more 
water would be able to condense. 
While H-NMR proves powerful as tool to analyze the local chemical and physical 
alterations, there has not been any conclusive evidence obtained from it. This method 
supports the idea of amorphous drug evolving into crystalline drug during quenching. Other 
data obtained from the H-NMR may imply a further evolution of amorphous drug with the 
induction of water condensation, or possibly an induced crystal size redistribution. 
 
 
 
 
 
 
 
 
51 
 
 
 
 
 
 
 
APPENDIX B 
 
PRELIMINARY RAMAN SPECTROSCOPY DATA 
 
 
 
 
 
  
52 
 
Raman spectroscopy is a noninvasive tool that was used to understand the influence 
of relative humidity on the molecular structure and orientation of drug, fenofibrate, in 
composites. Changes in drug structure, induced by the controlled condensation of water, 
provide clues to the change in amorphous and crystalline content within the composite. 
This spectroscopy is conducted with a Ph.D. candidate in Dr. Rob Walker’s laboratory 
group, Kyle Reeping, in the Chemistry and Biochemistry Department at Montana State 
University.  
Raman Spectroscopy provides information about the composition and molecular 
structure of compounds.18 It employs a laser and microscope to excite molecules within a 
substance, here the drug, silica tablet, and composite.18 A laser is directed through a 
microscope objective onto the material, which subsequently interacts with the laser with 
respect to molecular energy modes such as vibrations.19 The inelastically scattered light is 
filtered and analyzed, resulting in a spectrum of intensity versus Raman wavelength.19 The 
“Raman wavelength,” or “Raman shift,” is dependent on the laser used, as different 
vibrational modes are captured with different lasers.19 Due to this, only spectra obtained 
using the same laser and excitation times are comparable. Additionally, each unique peak 
corresponds to a different molecular arrangement, and thus different vibrational properties 
due to bond arrangements.18 This allows spectral peaks to be compared to known peak 
wavenumbers to identify the composition and structure. Unfortunately, if a spectral peak 
has not been conclusively identified, it is unlikely that it can be used to identify the 
composition and/or arrangement or a complex system conclusively. Due to the complicated 
nature of the spectra obtained, as well as the unknown identifiable peaks, in the following 
53 
 
experiments, only comparative analysis is conducted. While there is minimal literature 
about the exact identification of peaks in the spectrum, a paper published in 2009 suggested 
analysis of structural changes of the drug.20 Spectral peak widening of the composite in a 
varied relative humidity suggests a decrease in crystalline drug content.20 Additionally, if 
the wavenumber associated with the peak changes, it implies a change in the crystalline or 
amorphous form.20 
The difference between an unimbibed and imbibed tablet was examined using 
Raman spectroscopy as a baseline for future experiments. It is important to understand 
what changes in the spectrum are due to the drug, and what are due to the silica. To explore 
this, a silica tablet was slip cast and left in 0.0 relative humidity for three days. Another 
silica tablet was slip cast and imbibed with fenofibrate at 90oC. This composite was then 
wiped off with a tissue and placed in 0.0 relative humidity for three days. In all 
experiments, unless otherwise noted, a 633 nm laser was used and all samples were placed 
on top of a gold disc to restrict unwanted light refraction. Scans of the samples were taken 
every 15 seconds, in multiples of three before moving to the next sample. This was done 
to eliminate cosmic rays. If an abrupt signal appeared with a width less than one 
wavelength, that then disappeared after the next scan, it was labeled a cosmic ray and 
removed. The two spectra are displayed in Figure B.1., showing the complex nature of the 
composite as compared to the silica template. This plot allowed us to subtract out the signal 
from the silica, since we are only interested in the changes the fenofibrate is undergoing. 
 
 
54 
 
Figure B.1. Raman spectra of an unimbibed silica tablet and fenofibrate imbibed silica 
tablet, illustrating the difference in drug imbibition and complex nature of the system. 
 
 
The next spectrum needed was the difference between restricted and unrestricted 
fenofibrate. This was important to understand what spectral changes were due to the drug 
undergoing melting and recrystallization, and what were due to drug confinement in 
nanopores. To understand this, a slip cast silica tablet was imbibed as previously described, 
and placed in 0.0 relative humidity for three days. Additionally, fenofibrate was melted on 
a glass slide at 90oC, and the slide was subsequently moved to 0.0 relative humidity for 
three days. Raman spectra were then obtained for these two samples, as previously 
described. These spectra are displayed together, illustrating the effect confinement has on 
the drug in the system. There is a noticeably lower intensity in the Raman spectrum 
associated with the restricted drug. This depletion dilutes the effects of peak widening and 
narrowing, making conclusions difficult to draw.  
55 
 
 
Figure B.2. Raman spectra (633 nm) of a fenofibrate imbibed silica tablet coplotted with 
unconfined fenofibrate that underwent the same protocol, showing the intensity depletion 
of confined fenofibrate. 
 
 
While differential scanning calorimetry (DSC) proves useful, it is unable to provide 
insight into the molecular changes occurring when a tablet is subjected to 0.0 relative 
humidity and then varying relative humidity, without returning to 0.0 relative humidity. To 
investigate the effect this change in protocol had on the molecular structure, Raman 
spectroscopy was conducted on six different tablets as previously described. The difference 
in this protocol is that the tablets never returned to 0.0 relative humidity. In other words, 
they were imbibed, placed in 0.0 relative humidity for three days, then varying relative 
humidities for three days. They were then tested. In order to ensure no water evaporates 
off due to the humidity change between the chamber they were stored in and the testing 
chamber, the corresponding saturated salt solution was placed in the testing chamber for 
ten minutes to allow for equilibration. This was done in the order of lowest relative 
humidity to highest.  
56 
 
To support the hypothesis that crystallinity isn’t changing drastically in samples 
exposed to differing relative humidities, and to try to understand possible other molecular 
changes occurring, Raman spectroscopy was performed on six different tablets. The silica 
tablets were made as previously described – slip cast on gypsum. The porous silica tablets 
were then placed on melted fenofibrate, melted at 90oC, until fully imbibed, about 30 
minutes. The imbibed tablets were then removed with tweezers and quickly wiped off with 
tissue. They were then placed in a 0.0 relative humidity chamber for three days. After this, 
they were transferred to varying relative humidity chambers for three days. The following 
relative humidities were used: 0.0, 0.25, 0.43, 0.75, 0.91, and 1.0. All composites were 
finally moved back to the 0.0 relative humidity chamber for three days. Following this, 
they were transferred to the Raman spectroscopy facility.  
If the hypothesis that crystallinity is undergoing no drastic change, the peak widths 
and Raman wavelength corresponding to the maximum intensity won’t change. This is 
what happened, as shown in Figure B.3. The peaks are all similar in width and Raman 
wavelength, indicating no significant change in crystallinity was induced by varying the 
relative humidity. 
 
57 
 
 
Figure B.3. Raman spectrum (633 nm) of composites that underwent the protocol of 
imbibition, 0.0 relative humidity, varying relative humidity, then 0.0 relative humidity. 
These spectra show minimal differences in molecular composition and arrangement.  
 
 
 As previously elaborated, crystallinity changes would be indicated by changing 
peak width, and Raman wavelength number. Figure B.4 displays the spectra produced by 
these composites, and show no discernable changes with respect to varying relative 
humidities. This implies no drastic structural changes were induced by differing humidities.  
 
 
58 
 
 
Figure B.4. Raman spectra (633 nm) of fenofibrate imbibed silica tablets coplotted that are 
subjected to varying relative humidities. These composites are subjected to 0.0 relative 
humidity then varying relative humidities before testing. This shows no meaningful change 
in molecular arrangement with respect to relative humidity.   
 
 
While there were few notable differences in spectra of varying relative humidity 
within the same protocol, there were major differences between spectra of varying relative 
humidity with respect to protocol. As shown subsequently in Figure B.5, the spectra of a 
tablet at 1.0 relative humidity was examined across protocols. There is a dramatic depletion 
of intensity in the peaks seen in the spectra that went from 0.0 to 1.0 back to 0.0 relative 
humidity as compared to staying in 1.0 relative humidity. While it may appear as though 
signals disappear, this is not the case. The spectrum of these signals is dwarfed by the 
dominating spectrum of the protocol ending in 1.0 relative humidity. The signal in this 
spectrum occurring at about 2650 cm-1 is a cosmic ray, identified due to its near-zero width. 
The obvious diminished peak intensity and width in the protocol ending in 0.0 relative 
humidity, implies the composite ending in 1.0 humidity is composed of less crystalline 
structure. However, due to the inequality of peak intensity, it is difficult to compare exact 
59 
 
peak widths. The differences in spectra are from molecular changes of confined 
fenofibrate, so while there are no conclusions drawn it is clear the drug undergoes changes 
with the induction of water. It is also possible that structural changes are happening so 
slowly that an additional three days between imbibition and testing, in the protocol of 0.0, 
1.0, 0.0 relative humidity, allowing for more conformational changes.  
 
 
Figure B.5. Raman spectra (633 nm) of fenofibrate imbibed silica tablets that underwent 
differing protocols. This shows the depletion in intensity, implying an alteration in 
molecular drug arrangement in the composite that was exposed to 0.0 relative humidity, 
1.0 relative humidity, and 0.0 relative humidity again.  
 
 
System analysis using Raman spectroscopy proved useful in conveying molecular 
changes in fenofibrate restricted by pores, provided by colloidal silica, compared to 
unconfined drug. Raman spectroscopy also proved useful in gaining insight to the 
molecular changes induced by varying relative humidity composites were exposed to. Two 
different protocols were investigated. The first was exposing the composites to 0.0 relative 
humidity, then varying relative humidity, and finally 0.0 relative humidity again, all for 
60 
 
equal time. The second was exposing the composites to 0.0 relative humidity and then 
varying relative humidity, foregoing re-exposure to 0.0, both for equal time. While there 
are, seemingly, no drastic changes with respect to differing relative humidities within each 
protocol, there are definite changes in spectra with respect to protocols. Exposing a 
composite to non-zero relative humidity increases the peak intensity greatly.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
61 
 
 
 
 
 
 
 
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