THE RELATIVE EFFECT OF SOLUTE SIZE AND POLARITY ON THE DIFFUSION
COEFFICIENT IN ZERO-ORDER RELEASE THROUGH A POLYMER MEMBRANE
Vipul Bhat, Ranvir Bhatia, Katie Cavanaugh, Albert Chen, Edward Gelernt, Michael Hill-Oliva,
Remy Kassem, Jai Patel, Ruchit Patel, Nha-Uyen Pham, Jack Xiong, Eitan Zlatin
Advisor: Dr. David Cincotta
Lab Assistant: Suma Gondi
ABSTRACT
A kinetic process is considered zero-order if it proceeds at a constant rate independent of
time or concentration of substance. Although diffusion is intrinsically non-zero-order, the
process can be made pseudo-zero-order by allowing the solvent to evaporate through a polymer
membrane. The rates of pseudo-zero-order reactions do depend on reactant concentration, but
they maintain a constant rate over time, as it is a characteristic of true zero-order reactions. The
rate of diffusion is reflected in a substance’s diffusion coefficient, which relates flux to
concentration gradient independently of pressure, temperature, and membrane thickness. In this
experiment, various alkanes, ketones, and alcohols classes were allowed to diffuse through a
membrane of poly(ethylene-vinyl acetate). Average rate of zero-order solvent flux through the
membrane was used to compute diffusion coefficients. The data indicates that organic
compounds of the same polarity class tend to have increasing diffusion coefficients as the
molecular size increases and similarly sized compounds with increasing polarity had an
increasing diffusion coefficient. The results indicate that molecular size alone has an impact on
the ability to diffuse through a polymer membrane, but changes in polarity also had a great
impact on the diffusion coefficient.
INTRODUCTION
Diffusion and Fick’s Law
Diffusion is the random movement of molecules following a concentration gradient from
high to low concentration. In this experiment, a polymer membrane acts as a barrier that pure
substances have to diffuse through. As pure liquids, the solvents used in the experiment have a
constant concentration and therefore a constant vapor pressure inside the membrane covered jar.
This creates a chemical potential difference across the membrane with the solvent having a
constant chemical potential inside the membrane and the external environment having a chemical
potential of zero. A constant chemical potential difference is key in simulating a zero-order rate
of diffusion while effectively manipulating Fick’s laws of diffusion to determine diffusion
coefficient.
Diffusion can be affected by numerous other variables, such as the nature of the solution,
the nature of the membrane, and environmental conditions such as temperature affect diffusion in
different ways. In this experiment, organic solvents with varying sizes and polarities were
allowed to diffuse through a polymer membrane in order to observe differences in rates of
diffusion. This effect was quantified by calculating diffusion coefficients.
[5-1]
Fick’s law describes the relationship between the rate of diffusion, concentration
gradient, and surface area of the membrane as a solute diffuses across the membrane according
to equation 1:
𝐽 = −𝐷
𝜕∅
𝜕𝑥
[1]
where J is solvent flux across the membrane, D is the diffusion coefficient, ∂ϕ represents the
change in chemical potential, and ∂x represents the thickness of the polymer membrane (1). By
Raoult’s law, the vapor pressure of a liquid at a constant temperature remains constant, ensuring
the concentration of the liquid vapor attempting to exit the membrane will not change (2). The
constant value of ∂ϕ/∂x over time ensures that flux is directly proportional to diffusion
coefficient.
Controlled-Release Kinetics
Release of a compound can be controlled by introducing a membrane to induce pseudozero-order kinetics. Such kinetics have many different applications, most notably the release of
drugs and other pharmaceuticals into the bloodstream. Most non-controlled-release
pharmaceutical mechanisms involve the release of a large amount of drug into the bloodstream at
one time. The body slowly metabolizes the drug until its concentration falls below therapeutic
levels. In the absence of controlled-release mechanisms, plasma concentrations must fluctuate
between sub-therapeutic and potentially toxic levels in order for the drug to retain efficacy over
time. These limitations increase health risks for patients and require frequent re-administration of
medicines (3). In contrast, controlled-release systems maintain adequate drug concentration in
the bloodstream over extended periods of time. In such systems, polymeric coatings act as
permeable membranes through which therapeutic compounds diffuse at constant rates. In
addition to prolonging the timeframe of drug distribution, these controlled-release systems
maintain nearly constant drug levels within the ideal therapeutic window (Fig. 1), avoiding
potentially hazardous peaks in concentration following ingestion.
[5-2]
Figure 1 (Controlled Release Application): The dotted line represents the ideal plasma
concentration of a drug with an effective controlled-release mechanism over a period of time. By
contrast, the solid line represents the fluctuating concentrations of a drug that includes an
immediate-release mechanism. The peaks signify points of concentration in which the drug
levels are highest. As shown above, the peaks in concentration approach the drug’s toxicity
threshold (4).
Solubility Parameters
Hansen Solubility Parameters are used to identify the degree of solubility between two
compounds. Developed by Charles Hansen, this model provides a quantitative approach to
compare the miscibility of different compounds based on their respective intermolecular forces.
The model is based on the principle that “like dissolves like”; molecules with similar
intermolecular forces are compatible for dissolution. London dispersion forces, hydrogen
bonding, and dipole-dipole interactions of each compound are taken into account and factored
into a three-dimensional spherical graph created by Hansen (Fig. 2). If there exists a greater
difference among the intermolecular forces of the two compounds, a lower overall solubility
exists between them. The cohesive energy densities of the different intermolecular forces
between molecules of a substance are identified by δd (dispersion forces), δp (dipole forces), and
δh (hydrogen bonding). By comparing these values between substances, one can calculate an Ra
value seen in equation 3, which is defined as the distance between the two substances on the
three-dimensional Hansen graph. As a result, lower Ra values indicate greater solubility between
two substances. Dividing this Ra value by Ro (radius of interaction) of the substance dissolved
gives the value of the RED (the relative energy difference of the system) as seen in equation 4. If
the RED value for two substances is less than 1, then the two substances are miscible. If the RED
value is equal to 1, then the substances are partially soluble within each other. RED values
[5-3]
greater than 1 indicate substances that are insoluble within each other. Based on Graham’s law, it
is known that larger particles will diffuse more slowly than smaller particles; however, when
molecular size of a substance is different, so is its polarity. These solubility parameters help
determine the effect of this change in polarity on the diffusion of substances. By comparing RED
values, Ra values, and diffusion coefficients of the different substances used in the experiment
across the EVA membrane, one can observe the effect of polarity on a substance’s diffusion and
whether that factor is more or less significant than molecular size (5).
𝑅𝑎2 = 4(𝛿𝑑2 − 𝛿𝑑1 )2 + (𝛿𝑝2 − 𝛿𝑝1 )2 + (𝛿ℎ2 − 𝛿ℎ1 )2 [2]
𝑅𝐸𝐷 = 𝑅𝑎 ⁄𝑅𝑜 [3]
Figure 2 (Hansen Solubility Sphere): The graph of the solubility sphere of a substance in threedimensional Hansen space. The coordinates of the center of the sphere are determined by the
solubility parameters, while the radius of interaction determines the radius of the sphere (6).
Effusion and Graham’s Law
Effusion is defined as the movement of gas particles through a small hole. Graham’s Law
of effusion states that rate of effusion varies inversely with molar mass (7). Though Graham’s
Law is not directly applicable to the movement through a copolymer membrane as it considers
effusion rather than diffusion, it may still be relevant. Diffusion through a polymer such as EVA
requires small particles to pass through tightly packed polymer networks, which may be similar
to passing through many small holes. Therefore, effusion may serve as an approximate model for
diffusion through a polymer. Assuming that this process is analogous to diffusion, gases with
greater molar mass should diffuse more slowly through a polymer membrane than those with
smaller molar mass under constant temperature and pressure.
EVA Membranes
Poly(ethylene-vinyl acetate) (EVA) is used to create the polymer membranes through
which solutes can diffuse. The films are created by mixing the copolymer with toluene in an
Erlenmeyer flask on a hot plate in order to create a homogeneous solution. This mixture is used
to produce a semi-permeable membrane that can separate the solutes based on polarity,
[5-4]
molecular size, temperature, crystallinity, and intermolecular forces. Polyethylene is nonpolar
due to the fact that it contains only C-H bonds and carbon and hydrogen have a relatively low
electronegativity difference (Fig. 3). As more hydroxyl-containing polyvinyl acetate is added to
polyethylene, the polarity of the EVA mixture increases, allowing more polar solutes, such as
larger molecules with greater London dispersion forces, will likely diffuse across the membrane
at a faster rate. Conversely, the smaller molecules may diffuse across the membrane at even
quicker speeds as reflected in Graham’s Law. As the percentage of vinyl acetate in the
membrane decreases, the structure becomes more crystalline, precluding larger molecules from
diffusing through the rigid membrane as easily. Small molecules are unlikely to be greatly
affected by the percentage vinyl acetate of the membrane since both crystalline and amorphous
structures allow the small molecules to diffuse.
Figure 3 (Structure of EVA Components): The EVA polymer membrane is comprised of
polyethylene (a) and vinyl acetate (b). Polyethylene is a nonpolar membrane whereas vinyl
acetate is polar due to the highly electronegative carbonyl group (8).
Solutes
The goal of this experiment was to examine the effects of the size and the polarity of the
solutes on the diffusion coefficient. To establish a constant concentration gradient, pure liquids
were selected that would have a constant vapor pressure and therefore a constant chemical
potential. We chose three general classes of organic compounds to test: alkanes, ketones, and
alcohols. In each group, we chose four different compounds with ascending molecular size and
ensured sizes, based on molar mass, were consistent across the three groups. With this system,
we could compare not only the effect of different sizes, but also the effect across different
polarity classes. Alkanes are nonpolar saturated hydrocarbons that contain only single bonds; this
group is the most nonpolar out of the three. Ketones are hydrocarbons that have a carbonyl group
(C=O) in the middle of the chain. This group creates a net dipole; therefore, ketones are more
polar than the alkanes. Finally, alcohols are hydrocarbons that have a hydroxide (-OH) polar side
chain, so they are significantly more polar than the other two classes. The differences in the
structures of each hydrocarbon group give rise to differences in polarity, which affect the speed
at which the substances diffuse through a polymer membrane.
[5-5]
Previous Research
In 2013, the New Jersey Governor’s School in the Sciences’ controlled release kinetics
team looked at the effects of differing membrane composition on the relative rate of diffusion.
The team was able to achieve zero order release with alkanes and alcohols, and calculated the
diffusion coefficient to give an idea of the rate of diffusion. In their hypothesis, the scholars
predicted that an increase in the EVA composition of the membrane would increase the rate at
which a solute would diffuse across a membrane, which was supported by their data. They were
also able to determine that the crystallinity of the membrane affects the rate of diffusion more
than the polarity of the solute diffusing across the membrane. However, they were unable to
study the effects that the size and polarity of the solute have on the diffusion coefficient. They
observed changes when they varied the size of the compound, but they focused more on
manipulating the composition of the membrane. From the data that they had, they calculated
some diffusion coefficients and saw an increase in the coefficient as the size of the molecule
increased but the results were inconclusive. They speculated that this trend of data was due to the
condensability of the liquid, but they could not definitively explain what occurred (9).
In 2014, the Governor’s School of the Sciences’ controlled-release
kinetics team tested the effects of multiple variables on the rate at which a pure solute diffuses
through a polymer membrane. The scholars also concluded that the use of a pure liquid in fact
could create pseudo-zero order kinetics. However, many of their substances diffused at an
extremely slow rate, or did not diffuse at all. Therefore this team’s experiments focused on
determining the relative rates of diffusion through the membrane and what could be done to
increase this rate. Building upon the research from the previous two years, specific solutes were
selected where zero order diffusion is possible so that direct conclusions could be drawn about
the effect solute size and polarity have on the diffusion coefficient (10).
HYPOTHESIS
Larger organic molecules will diffuse through an EVA membrane at a slower rate than
smaller organic molecules due to an inverse relationship between particle size and diffusion rate,
and will thus have lower diffusion coefficients. Although increased polarity increases a
compound’s solubility in the polar polymer, increased molecular size will prove more significant
in affecting diffusion coefficient than polarity will, so longer-chain organic compounds will have
lower diffusion coefficients in spite of their increased polarity.
METHODS AND MATERIALS
Synthesis of Polymer Membranes
Membranes were made from a solution of 75% toluene and 25% EVA by mass. The EVA
used was 25% polyvinyl acetate and 75% polyethylene by mass. The mixture was then covered
with a cork, stirred, and heated until rendered homogeneous. Additionally, the cork was wrapped
in Saran wrap to prevent any particles from the cork to fall into the Erlenmeyer flask in which
the solution was made. Then a calendar, a rectangular instrument with a thin slit through which
mixture can flow, was used to spread the mixture onto release paper at a thickness of 0.025
inches (Fig. 4). This thickness was found to be ideal for creating the films as well as for the
[5-6]
membranes in the experiments. The release paper
was taped at the corners to glass sheets to ensure it
would stay flat and not bend the finished
membrane. The calendar was placed at the top of
the release paper and the solution was poured at the
top of the calendar. Then the calendar was pulled at
a steady and constant rate in order to try to prevent
uneven thicknesses throughout the film and to avoid
stretching the film that passed through the slit. It
was often necessary to heat and stir the solution
before making each film to limit the formation of
bubbles in the solution. Afterwards, the membranes
were placed in the fume hood to dry. It was
Figure 4: The calendar is pulled across
important that the preparation of the solutions and
the release paper to produce films.
the films, as well as the creation of the films, be
done in the fume hoods because the fumes from the
toluene solutions were extremely pungent. The
films were then dried additionally in an oven overnight at 60°C. Once the membranes cured,
their thicknesses were measured with a micrometer. Once the micrometer was found to be
inconsistent for these measurements, an average thickness of several EVA membranes, measured
using a more accurate method involving the masses, lengths, widths and densities of the
membranes, was used as a standard for the experiments that had already been completed. It was
appropriate to use an average in this situation because all the membranes measured in this
fashion yielded very similar measurements.
Solutions
The organic compounds tested had varying size and polarity, coming from alkane,
ketone, and alcohol polarity classes. Within each class, four compounds of different sizes were
tested (see Table 1). Alkanes tested were pentane, n-hexane, heptane, and n-octane. The
molecules chosen for the ketone group were 2-butanone, 2-pentanone, 2-hexanone, and 2heptanone. Similarly, the molecules chosen for the alcohol group were 1-butanol, 1-pentanol, 1hexanol, and 1-heptanol. The smallest molecules in the polarity classes had approximately the
same molecular weight and the molecular weight changed by approximately the same amount
with the addition of each carbon atom to the compound. The alcohols are highly polar due to
their hydroxyl groups, while the double-bonded oxygen gives ketones slight polarity. Alkanes
are the least polar of the three classes. The compounds were added directly to the apparatus
without dilution.
Table 1: Selected Organic Compounds
Alkanes
Pentane
(72.15 g/mol)
n-Hexane
(86.18 g/mol)
Heptane
(100.21 g/mol)
n-Octane
(114.23 g/mol)
Ketones
2-Butanone
(72.11 g/mol)
2-Pentanone
(86.13 g/mol)
2-Hexanone
(100.16 g/mol)
2-Heptanone
(114.18 g/mol)
[5-7]
Alcohols
1-Butanol
(74.12 g/mol)
1-Pentanol
(88.15 g/mol)
1-Hexanol
(102.18 g/mol)
1-Heptanol
(116.20 g/mol)
The molecules increase in molecular size from left to right and increase in polarity from top to
bottom.
Experimental Design
The long rectangular membranes produced by the filmmaking process were cut into
squares of varying dimensions, with widths and lengths slightly larger than the diameter of the
Mason jar, in order to ensure a better fit. The oversized edges gave the lid of the Mason jar a
surface to grip onto and twist, so sealing the lid shut did not distort the open surface of the
membrane the solution was intended to diffuse across. The membrane squares were stretched
taut over the rim of the jar, and the lid, with a silicone ring fitted inside the rim to ensure an
airtight seal, was placed over the membrane and screwed tight. This setup produced a consistent
membrane surface area for the solutions to diffuse across into the air and also produced a
consistent seal. These Mason jars were filled with 10 mL of organic compound solution, and
labeled with a batch number, the compound inside, and the properties of the membrane.
Data Collection
Figure 5 (Experimental Setup): (a) A computer was installed with time lapse software and
linked to a webcam elevated on a ring stand (b) Four mass balances were placed in the Field of
View (FoV) of the webcam (c) The webcam software took a picture of the array every 10
minutes
The flux of the solvent through the membrane was determined via gravimetric analysis.
The membrane-covered jars of solvent were placed on balances (Fig. 5). A webcam was used to
photograph the masses of the compound-containing jars at 10-minute intervals to determine
solvent evaporation over time. A thermometer was also included in the photographs to ensure
accurate temperature measurements over multi-day experiments. This setup allowed for accurate
[5-8]
data collection over significant time intervals, permitting unambiguous determination of
evaporation rate. In addition, the setup was easily scalable, allowing for as many as ten
compounds to be analyzed on two computers at any given time.
Determination of Diffusion Coefficient
Data from gravimetric analysis were used to determine diffusion coefficient by algebraic
rearrangement of Fick’s law to give equation 4:
𝐷 = −𝐽
𝜕𝑥
𝜕𝜙
[4]
The values in the equation were obtained as follows:
J: Flux of solvent through the membrane was based on the mass of solvent lost to evaporation,
the area of the exposed membrane, and the time over which the change in mass was measured.
The slope of the line of best fit for the measured masses of the compounds at half-hour intervals
was taken as the rate of evaporation of solvent in g/half hr. The slope was multiplied by 2 to get
g/hr and then divided by the solvent’s molar mass, and the surface area of the membrane to
obtain flux in units of mol m-2 hr-1.
∂x: Membrane thickness was determined initially by micrometer measurement. However, when
this method proved imprecise, a new technique was developed. A square section of each film
was cut and weighed, and its surface area was measured. The mass was divided by the known
density of the copolymer, 0.948g/mL (11), to obtain volume, which was divided by surface area
to determine thickness. As this new technique was developed after several data sets were already
collected, thickness of several different membranes was measured and averaged to approximate
the thicknesses of the membranes previously used. The result was 6.6μm, and the values
measured to calculate this average had relatively little variance.
∂ϕ: Concentration of gaseous solvent was determined by algebraic rearrangement of the ideal
gas law, n/V=P/RT. Temperature was held approximately constant at 22±1°C. Vapor pressure
was approximated from the Antoine equation as described below. This approximate vapor
pressure was divided by 22°C and the ideal gas constant to obtain gas concentration.
Antoine Equation
The Antoine Equation given in equation 5 can be used to approximate vapor pressure for a given
compound at a given temperature:
𝑙𝑜𝑔10 𝑝 = 𝐴 −
𝐵
𝐶+𝑇
[5]
where p is vapor pressure of the compound, T is temperature, and A, B, and C are compoundspecific constants (12). This equation is generally accurate within 10% for temperatures ranging
from the triple point to the critical point.
[5-9]
RESULTS
The masses of the experimental compounds were collected at half-hour intervals from
time lapse photographs and entered into Microsoft Excel to track diffusion over time (Fig. 6).
Most data sets demonstrated nearly perfectly linear diffusion, while others had more noticeable
variances; nonetheless, the data showed excellent correlation with zero-order diffusion (r2>0.99).
Some of the liquids with higher diffusion coefficients had masses that suddenly leveled off and
stopped displaying zero order diffusion rates. This was caused by the complete evaporation of all
the liquid, preventing the vapor pressure from remaining constant. Such data was excluded when
determining the line of best fit and r2 values.
Figure 6 (Primary Data for n-Octane): The gravimetric data collected for n-Octane
Compounds
Table 2 shows the various compounds that were tested, sorted by polarity class and
molecular size, and the average diffusion coefficient that was calculated. By manipulating Fick’s
law and taking measurements of the membrane thickness, vapor pressure, and mass lost over the
time period (Fig. 6), the diffusion coefficients for the various compounds could be calculated.
For the 1-hexanol and 1-heptanol, we were unable to collect reliable data from the second trial of
each substance. The data was very erratic and could not be quantifiable so the average diffusion
coefficient for those two substances was calculated using only one trial. The diffusion
[5-10]
coefficients were plotted and a linear relationship was observed, with the diffusion coefficient
increasing along with the molecular size. For all three polarity classes of compounds, a linear,
positive correlation was seen between molecular size and the diffusion coefficient (Fig. 7).
Table 2: Diffusion Coefficients of the Various Compounds
Substance
Average Flux
(g m-2 hr-1)
Thickness of
Membrane (μm)
5.685
66
Average Diffusion
Coefficient (m2 s-1)
Alkanes
Pentane Trial 1
16.05
Pentane Trial 2
6.005
66
n-Hexane Trial 1
1.599
66
15.90
n-Hexane Trial 2
1.736
66
Heptane Trial 1
0.5095
66
18.12
Heptane Trial 2
0.6101
66
n-Octane Trial 1
0.1820
66
19.26
n-Octane Trial 2
0.1743
66
1.068
66
Ketones
2-Butanone Trial 1
16.63
2-Butanone Trial 2
1.188
66
2-Pentanone Trial 1
0.4929
66
18.00
2-Pentanone Trial 2
0.3962
66
2-Hexanone Trial 1
0.1778
66
59.24
2-Hexanone Trial 2
0.1226
66
[5-11]
2-Heptanone Trial 1
0.04763
66
58.23
2-Heptanone Trial 2
0.06837
66
0.1243
78
Alcohols
1-Butanol Trial 1
34.012
1-Butanol Trial 2
0.09231
78
1-Pentanol Trial 1
0.07065
78
58.74
1-Pentanol Trial 2
0.02985
78
1-Hexanol Trial 1
0.02232
78
76.51
1-Heptanol Trial 1
0.009814
78
145.5
[5-12]
Figure 7 (Diffusion Coefficient versus Molar Mass): The effect on the diffusion coefficient as
the molar mass increases. Alkanes, ketones, and alcohols are on the same graph and linear trend
lines were applied
We were also able to plot the diffusion coefficient of compounds that have similar
molecular sizes but different polarities (Fig. 8). For example, the substances between 72 and 75
g/mol were pentane, 2-butanone, and 2-butanol. This allowed us to compare the effect polarity
had on the diffusion coefficient when the mass was kept constant.
Figure 8 (Diffusion Coefficient versus Polarity of Substance): Similarly sized substances
were placed in mass classes together and the diffusion coefficient was then plotted on the graph.
72-75 g/mol includes pentane, 2-butanone, 1-butanol, 86-89 g/mol includes n-hexane, 2pentanone, 1-pentanol, 100-103 g/mol includes heptane, 2-hexanone, 1-hexanol, and 114-117
g/mol includes n-octane, 2-heptanone, 1-heptanol
DISCUSSION
Analysis
Across all organic compounds, despite varying polarities and size, pseudo-zero-order
diffusion was achieved. In plots of the mass data points for all the samples, a constant linear
slope was observed. The magnitude of the mass lost for diffusing substances along with
measurements of vapor pressure and membrane thickness allowed us to calculate diffusion
[5-13]
coefficients for the substances. Using the diffusion coefficients, we were able to compare the rate
of diffusion through the membrane, as these are directly proportional quantities.
Analysis of the data reveals that there is a positive correlation between the size of the
molecule and the diffusion coefficient. For all three classes of compounds, the trend line for the
diffusion coefficients had a positive slope (Fig. 7). At the same time, we compared the diffusion
coefficients across polarity classes for similarly sized molecules. We observed that overall, as the
polarity of the molecule increased, the diffusion coefficient increased as well (Fig. 8). Therefore,
we can conclude with the data collected that the rate of diffusion for the molecules increased as
the molecular size as well as the polarity increased.
Looking at the graphs of the diffusion coefficients for each of the solution classes, there
are interesting trends that can be seen. The alkanes show a clear linear increase in the diffusion
coefficient proportional to increases in molar mass. A linear trend line was applied to the graph
of ketone diffusion coefficients, although the data more closely reflected a logistic curve. The
diffusion coefficient of 2-pentanone is drastically different than the coefficient of 2-hexanone
and there is not a proportional increase in the coefficient as the size of the molecule increases at a
constant rate. For the alcohols, a linear trend line was applied to the graph but the trend looks
almost exponential. There was not a proportional increase in the diffusion coefficient as the size
of the molecule increased for the alcohols. Also, when comparing molecules that have similar
molecular sizes but different polarities, an interesting trend was seen in the diffusion coefficient
as the molecular size class increased (Fig. 8). For molecules that were between 72 and 75 g/mol,
the differences in diffusion coefficient were not that drastic even though the polarities of the
molecules were very different. However, on the upper end of the size class, between 114 and 117
g/mol, there were large differences in the diffusion coefficient for molecules with different
polarities. This seems to indicate that as the molar mass increases, the effect that polarity has on
the diffusion coefficient increases as well. This might be explained by the fact that larger
molecules have greater dispersion forces and that along with the functional groups on molecules
like the ketones and alcohols might result in an effect that heavily impacts the diffusion
coefficient.
Our hypothesis that an increase in molecular size would decrease the diffusion coefficient
while polarity of the molecules would have a negligible effect was disproven by our results. One
possible explanation of the results is the increased polarity because of the greater dispersion
forces in larger molecules. This is quantified by the Ra values of the compounds relative to the
25% EVA membrane that we used (Table 5). For example, the alkanes increase in size by adding
one more carbon atom to the chain. As the size increases, as seen in the table, the Ra value of the
alkane decreases, meaning that it is becoming more compatible with the partially polar
membrane. If it is becoming more compatible, there must be a change in the overall polarity of
the molecule as it is compatible with a relatively polar membrane. This change in polarity can be
explained by the increasing dispersion forces as the molecule increases in size. Because the
larger molecule becomes more compatible with the membrane in terms of its polarity, it diffuses
through the membrane much more quickly and therefore has a higher diffusion coefficient than
smaller molecules with smaller dispersion coefficients.
[5-14]
Solubility Parameter Analysis
Table 5: Ra values of tested organic compounds in a 25% EVA membrane. These values were
calculated based on solubility parameters obtained from previous research.
Alkane
Ra
Ketone
Ra
Alcohol
Ra
Pentane
10.1
2-Butanone
5.6
1-Butanol
9.5
n-Hexane
9.7
2-Pentanone
4.7
1-Pentanol
7.8
Heptane
9.3
2-Hexanone
5.3
1-Hexanol
6.6
n-Octane
9.1
2-Heptanone
3.9
1-Heptanol
5.7
Figure 9 (Diffusion Coefficient versus the Ra Value): The graph shows how an increase in the
Ra value corresponds to a decrease in the diffusion coefficient
The solubility parameters for alkanes, ketones, and alcohols all provided additional proof
for our conclusions. In general, as the molecular size of the compound increased, the Ra value
decreased, which shows that the larger molecules are more miscible in the EVA membranes that
we produced (Table 5). The values were calculated based on solubility parameters that were
empirically determined (13) (14). Since compounds with lower Ra values are more compatible
with the membrane, they should be able to diffuse faster and should have a higher diffusion
[5-15]
coefficient (Fig. 9). For very polar molecules like the alcohols, the change in Ra is drastic as
compared to that of the alkanes so the diffusion coefficient changes much more drastically for
the alcohols than the alkanes. Thus, according to the Ra values of the alkanes, ketones, and the
alcohols, the substances with a greater molecular size should have a higher diffusion coefficient.
This supports our data, which shows a direct correlation between molecular size and the
diffusion coefficient. The larger substances have more electrons, so they have a higher dispersion
component and a higher overall polarity. The change in the components of the larger substances
makes the substance more similar to the 25% EVA membrane. As a result, it is likely that the
change in dispersion forces that is associated with the change in molecular size has a greater
impact on increasing the diffusion of the substance than the effect of the increase in molecular
size itself has on reducing the diffusion.
Comparison with Previous Experiments
In 2013, the controlled release kinetics team at the New Jersey Governor’s School in the
Sciences tried to draw some conclusions regarding the relationship between molecular size and
the diffusion coefficient. Although they did not have enough data to draw a conclusion between
the two, with what they had, they saw a similar trend: as the molecular size increased for some of
the compounds they looked at, the diffusion coefficient increased. On the other hand, the data
from the 2013 said that the polarity of the molecules did not have much of an effect on the
diffusion coefficient while we observed the opposite. The polarity of the molecules had a
significant effect on the diffusion coefficient, especially when comparing a nonpolar alkane to a
very polar alcohol. These results can logically be explained by the affinity of substances for
those similar in polarity, in this case a polar membrane with a polar molecule (9).
Possible Sources of Error
The membranes used in trials of alkanes and ketones were measured using a micrometer.
This micrometer was inaccurate because it only measured a small portion of the total membrane
and gave significantly different measurements for the same membrane when used more than
once. Although the membranes may have not been completely uniform, such vast differences in
the micrometer measurements reflect an imprecise tool. For the alcohols, the membrane
thicknesses were measured using the known density, mass, and cross-sectional area of the
membrane. Then, several membrane thicknesses were averaged and used as a standard thickness
for the alkane and ketone membranes. Because not every film had smooth edges, the
measurements of their dimensions and membrane thicknesses may have been slightly inaccurate,
which resulted in an imperfect standard membrane thickness. Considering membrane thickness is
a factor in the calculation of the diffusion coefficient, it may have caused slight variations in the
results.
The balances in the room might have been affected by changes in airflow throughout the
course of the experiment. Mass changes are relatively minute as the substance is diffusing
through the membrane, so subtle changes in the air could cause the balances to fluctuate. Some
of the substances tested, such as the larger ketones and alcohols, had low vapor pressures.
Because of this, the chemical potential across the membrane is very low and there is a very small
change in mass over the course of the experiment. This, combined with changes in the
environment, can cause great fluctuation in the balances and therefore affect the calculations for
[5-16]
the diffusion coefficient. For example, for the 1-hexanol and the 1-heptanol, there was only one
trial for each compound because only one trial resulted in reliable data. Some of the trials that the
team could not use showed an increase in the mass of the jars over the course of the experiment,
which is clearly incorrect.
Future Studies
The experiment confirmed previous years’ research that use of pure liquids allows for
controlled release of substances even with relatively small vapor pressures. Further studies could
determine methods to approximate zero order release with solutions that have a low vapor
pressure, ionic solutions, and mixtures of liquids. Substances like alcohols that have very low
vapor pressures have diffusion coefficients that are difficult to determine because of the very
small change in mass over the course of days. Future experiments should look into other
techniques that can more accurately quantify the diffusion of a substance that has a very low
vapor pressure. Mixtures of liquids prove to be very tricky because different liquids have
different vapor pressures, which complicates keeping concentration constant over the entire
period of time. Different vapor pressures mean different compounds diffuse out at different
speeds, which would change the concentration. Future studies could also look into zero-order
diffusion of larger and more complicated substances that can be more directly applicable to the
pharmaceutical and agricultural industry.
The team focused on determining the relative rates of diffusion of pure liquids through
25% EVA membranes. Additional studies could determine if the same conclusions hold for
different concentrations of EVA films. Films with higher concentrations of EVA are more
amorphous and have more gaps between polymer molecules that allow solutes to diffuse. This
could increase the correlation between molar mass and diffusion coefficient, as the lack of large
holes in the amorphous regions may limit the diffusion of the larger molecules. Additionally,
films with higher concentrations of EVA are more polar, increasing the effect of polarity on
diffusion. Membranes were made from a solution of 75% toluene and 25% solids (vinyl acetate
and polyethylene) by mass. Additional studies could determine if there is a better concentration
of solids in the films to use in order to create films with less variation in thickness.
The team also encountered many limitations in the filmmaking process. First, the films
were not completely uniform. Many of the films were of inconsistent thickness, which led to
varying results in the calculations. Future teams can try to develop methods to ensure the
consistency of the membrane thicknesses, allowing for more precise calculations, or techniques
for more precise measurement of the films, perhaps through the use of an electronic micrometer.
Additionally, further studies can refine the measurements used to calculate the diffusion
coefficient. The method used by the team failed to account for variations in thickness, which
could have affected the diffusion coefficients.
CONCLUSION
This experiment achieved zero-order kinetics with a constant rate of diffusion across an
EVA membrane. The success of previous groups in achieving zero-order kinetics allowed for the
deeper investigation into the relationships between size, polarity, and the diffusion coefficient.
Modifications in the setup of the jar and membrane as well as the new data recording setup
[5-17]
allowed the team to collect more data than any other previous controlled release kinetics group
while increasing the overall success of the trials. The hypothesis was rejected because as the
molecular size increased, the diffusion coefficient increased and polarity made a significant
difference on the diffusion coefficient. For the alkanes, there was a proportional increase in the
diffusion coefficient as the molecular size increased, but for the ketones and alcohols, this same
proportional increase was not observed. When comparing similarly sized molecules with
different polarities, at small molar masses, the difference in the diffusion coefficients were not
very different but at larger molar masses, there was a much greater difference. Hansen solubility
parameters helped to explain these phenomena by providing a numerical basis for the increase in
diffusion coefficient for similarly sized but more polar molecules. For molecules with very low
vapor pressures, trials were very unreliable, meriting further work in improving the reliability of
measured flux of substances with low vapor pressures. Overall, the results obtained validate the
new setup and recording protocols while giving concrete information about the relationship
between the size and polarity of the molecules and the diffusion coefficient.
REFERENCES
1. Conrad S.C. and Kamholz S.K. Fick’s law of diffusion [Internet][cited 2015 Jul 27]
Available from: http://www.usc.edu/dept/biomed/bme403/Section_1/fick.html
2. Clark J.M. and Ly I.L. and Khan S.K. Raoult’s law [Internet] [cited 2015 Jul 27]
Available from:
http://chemwiki.ucdavis.edu/Physical_Chemistry/Physical_Properties_of_Matter/Solutio
ns_and_Mixtures/Ideal_Solutions/Changes_In_Vapor_Pressure,_Raoult's_Law
3. Gokhale A.G. Acheiving zero order release kinetics using multi-step diffusion based drug
delivery [Internet] [cited 2015 Jul 27] Available from:
http://www.pharmtech.com/achieving-zero-order-release-kinetics-using-multi-stepdiffusion-based-drug-delivery
4. Ghosal K.G. Freeman B.D. 1994. Gas separation using polymer membranes: an
overview. Polymers for advanced technologies. Vol(5):673-697.
5. Hansen C.H. 2000 Hansen solubility parameters: a user's handbook 2nd ed Boca Raton
Taylor & Francis Group, LLC 519 p.
6. Burke J. 1984. Solubility Parameters: Theory and Application. The Book and Paper
Group Annual of the American Institute for Conservation of Historic and Artistic Works
[Internet]. [2011 Aug 3, cited 2013 Jul 30] Vol Three 1984. Available from:
http://cool.conservation-us.org/coolaic/sg/bpg/annual/v03/bp03-04.html
7. Graham’s law [Internet][cited 2015 Jul 27] Available from:
http://www.chemteam.info/GasLaw/Gas-Graham.html
8. Andrew J.P. Handbook of polyethylene: structures, properties, and applications.
[Internet] [cited 2014 Jul 27] Available from:
http://books.google.com/books?hl=en&lr=&id=OPuWyxwJwJwC&oi=fnd&pg=PR5&dq
=structure+of+polyethlyene&ots=VstmHfCXeu&sig=I7ZRFIih_qNNfVSVmtRLn7CztF
Q#v=onepage&q=structure%20of%20polyethlyene&f=false
9. Dormier AD et al. Relative influences of polarity and crystallinity on zero-order kinetic
release through a polymer membrane. New Jersey Governor's School in the Sciences,
2013. [Print] [cited 2015 Jul 29].
[5-18]
10. Balasubramanian RB et al. The effect of solute and membrane polarity in creating a
pseudo-zero-order controlled release process. New Jersey Governor's School in the
Sciences, 2014. [Print] [cited 2015 Jul 29].
11. DuPontTM Elvax® EVA Resins for adhesives, sealants and wax blends. [Internet] [cited
2015 Jul 27] Available from: http://www.dupont.com//content/dam/dupont/products-andservices/packaging-materials-and-solutions/packaging-materials-and-solutionslanding/documents/elvax_adhesives_wax_blends.pdf
12. Antoinne coefficients [Internet] [cited 2015 Jul 29] Available from:
http://www.eng.auburn.edu/~drmills/mans486/Diffusion%20Tube/Antoine_coefficient_t
able.PDF
13. Asahi Glass Company Method for producing fluorinated copolymer composition, coating
composition, article having coating film, and molded product. [Internet] [cited 2015 Jul
27] Available from: http://www.google.com/patents/US20130053493
14. Diversified Enterprises Surface tension, Hansen solubility parameters, molar volume,
enthalpy of evaporation, and molecular weight of selected liquids [Internet] [cited 2015
Jul 29] Available from : http://www.accudynetest.com/solubility_table.html
[5-19]