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 CincottaLab 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 pseudo-zero-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 (δ d 2−δd 1)

2+(δ p 2−δ p 1)2+(δ h2−δ h1)

2 [2]RED=Ra/ Ro [3]

Figure 2 (Hansen Solubility Sphere): The graph of the solubility sphere of a substance in three-dimensional 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, molecular size, temperature, crystallinity, and intermolecular forces. Polyethylene is nonpolar

[5-4]

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.

Previous Research

[5-5]

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 membranes in the experiments. The release paper was taped at the corners to glass sheets to

[5-6]

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 important that the preparation of the solutions and 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 2-heptanone. Similarly, the molecules chosen for the alcohol group were 1-butanol, 1-pentanol, 1-hexanol, 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)

Alcohols 1-Butanol 1-Pentanol 1-Hexanol 1-Heptanol

[5-7]

(74.12 g/mol) (88.15 g/mol) (102.18 g/mol) (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 data collection over significant time intervals, permitting unambiguous determination of

[5-8]

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− BC+T

¿ [5]

where p is vapor pressure of the compound, T is temperature, and A, B, and C are compound-specific 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 coefficients were plotted and a linear relationship was observed, with the diffusion coefficient

[5-10]

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)

Average Diffusion Coefficient (m2 s-1)

Alkanes

Pentane Trial 1 5.685 6616.05

Pentane Trial 2 6.005 66

n-Hexane Trial 1 1.599 6615.90

n-Hexane Trial 2 1.736 66

Heptane Trial 1 0.5095 6618.12

Heptane Trial 2 0.6101 66

n-Octane Trial 1 0.1820 6619.26

n-Octane Trial 2 0.1743 66

Ketones

2-Butanone Trial 1 1.068 6616.63

2-Butanone Trial 2 1.188 66

2-Pentanone Trial 1 0.4929 6618.00

2-Pentanone Trial 2 0.3962 66

2-Hexanone Trial 1 0.1778 6659.24

2-Hexanone Trial 2 0.1226 66

2-Heptanone Trial 1 0.04763 6658.23

2-Heptanone Trial 2 0.06837 66

Alcohols

1-Butanol Trial 1 0.1243 7834.012

1-Butanol Trial 2 0.09231 78

1-Pentanol Trial 1 0.07065 78 58.74

[5-11]

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

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.

[5-12]

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, 2-pentanone, 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 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,

[5-13]

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.

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.

[5-14]

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 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

[5-15]

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 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

[5-16]

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 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

[5-17]

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/Solutions_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-step-diffusion-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].

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-and-services/packaging-materials-and-solutions/packaging-materials-and-solutions-landing/documents/elvax_adhesives_wax_blends.pdf

[5-18]

12. Antoinne coefficients [Internet] [cited 2015 Jul 29] Available from: http://www.eng.auburn.edu/~drmills/mans486/Diffusion%20Tube/Antoine_coefficient_table.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]