Type B gelatin (225 Bloom, Sigma Chemical Company) was extracted from bovine skin. The gelatin solution was prepared by dissolving 20 g of gelatin in 100 mL of deionized water at 70˚C in water bath. After dissolving the solution completely, 20% (g/g of gelatin) of glycerin was added as a plasticizer and stirred for 30 min. For the preparation of antimicrobial film, 0.2%, 0.5% and 1.0% potassium sorbate (g/g of gelatin) was added with glycerin. These final gelatin solutions were poured onto a Teflon coated glass plate measuring 27 × 27 cm. The plates were dried at 25˚C for 48 h, and then they were carefully removed from the glass plate. The prepared films were conditioned at 25˚C and 50% RH in a controlled environmental chamber for 48 h before testing. Film thickness was measured using a hand-held micrometer and was expressed as an average of 9 readings for each sample, 1 at the center and 8 around the perimeter.

The diffusion experiments of potassium sorbate from gelatin films were conducted at 3 different pH levels (3.5, 5.0, and 6.8). Five grams of each sample were immersed in water in conical flask, which were shaken at 150 rpm by means of an orbital shaker at 25˚C. During the release experiments, samples of water were drawn from the beaker at certain times, and using a UV spectrophotometer at 254 nm to measure the amount of released potassium sorbate. The diffusion experiments of 0.5% potassium sorbate from film were conducted at temperatures (5˚C, 25˚C and 35˚C).

The diffusivity of potassium sorbate from the film into water was determined by Fick’s second law, as follows [12]:

where C is the concentration of potassium sorbate, D is the diffusivity, x is the space coordinate in the direction of transport; and t is time.

For a film of thickness l (0 < x ≤ l), the following assumptions were made: initially, the distribution of potassium sorbate in the films was uniform and the concentration of potassium sorbate in water and on the film boundaries (x = 0 and 1) was zero. Under the previous assumptions, a classical solution for a plane sheet of thickness l is given by

where C₀ is initial concentration of potassium sorbate in film.

The fractional release as a function of time is obtained by integrating Equation (2) over the thickness of the film [8]:

Equation (3) was used to simulate the theoretical diffusion curve.

For early stages (M_t/M_∞ < 2/3) of diffusion processes, the diffusivity of this work was calculated with the following Equation (4):

where k is the slope of the linear regression of M_t/M_∞ versus t^1/2 .

The mechanism related to diffusion behavior for a plane sheet (flat film) system was investigated using the following equation [13] [14]:

where M_t/M_∞ is the fractional release of the potassium sorbate, t is the release time, k is a constant that depends on the macromolecular network characteristics of the film in addition to its interaction with the solution, and n is the diffusion exponent characteristic of the release mechanism.

Fickian diffusion is characterized by n = 0.5 which means diffusion is controlled by the diffusion coefficient (Case I system). A value of n = 1 shows Case II and diffusion is very rapid compared with the relaxation process of polymer. Non-Fickian or anomalous diffusion is denoted by 0.5 < n < 1. Values of n ˃ 1 indicate Super Case II transport [12].

Swelling was determined as follows. Antibacterial gelatin samples (diameter 3 mm) were dried at reduced pressure for 1 day, and weighed (W_dry). The films were swollen in pH 3.5, 5.0 and 6.8 for a certain time at 25˚C, blotted with a tissue, and weighed again (W_s). Experiments were carried out in triplicate. The swelling (S) was calculated as:

Figure 1 shows fractional mass release from diffusion tests at pH 6.8 under various potassium sorbate concentration. All release curves were similar in shape, although diffusion rates varied with potassium sorbate concentration. The detected amount of potassium sorbate migrated into the diffusion solution consistently increased with time. The diffusion coefficients (D) calculated in this study with the early stage method (Equation (4)) are summarized in Table 1, which are in the order of 10⁻¹² m²/s. Table 1 shows that with increase of the potassium sorbate concentration, the diffusion coefficient of potassium sorbate increases. The transfer kinetics of diffusing potassium sorbate molecules depends greatly on the structure of the matrix. The addition of potassium sorbate increased the hydrophilic of gelatin film, the more concentration of potassium sorbate, the more hydrophilic. The hydrophilic of the matrix promotes potassium sorbate to migrate into water. Hence, an increase in potassium sorbate concentration results in higher diffusion coefficients of potassium sorbate.

Figure 2 shows the mechanism of different concentration of potassium sorbate diffusion in gelatin film. The n values calculated from Figure 2 in this study with Equation (5) are summarized in Table 1. The estimated n values are in the range from 0.43 to 0.52 and demonstrate that Fickian diffusion is the predominant mechanism of this release.

Diffusion coefficients of 0.5% potassium sorbate in gelatin films at different temperatures are shown in Table 2.

It can be seen that diffusivity coefficient increases with the temperature. When the temperature was raised from 5˚C to 35˚C, diffusion coefficient increased about 4 times for potassium sorbate in gelatin film.

Activation energy E_a can be calculated from the Arrhenius activation energy model,

where D is the diffusion coefficient, D₀ is a constant, E_a is activation energy for the diffusion process (J/mol), R is universal gas constant (J/mol K), and T is absolute temperature (K).

The Arrhenius plots is derived from logarithmic transform of Equation (6) and shown in Figure 3, which indicates significant effect of temperature on diffusion with the high correlation coefficient values (r² ˃ 0.95). E_a is 31.05 kJ/mol calculated from the plot.

Figure 4 is swelling behavior of 0.5% potassium sorbate gelatin film in different receiving solution pH values. It can be seen that the film has obvious swelling behavior, and swells slowly after the initial stage of quick swelling, finally achieves swelling balance. The film has the higher swelling rate in pH 3.5 than in pH 5.0 and pH 6.8. The receiving solution pH value has effect on swelling rate of antibacterial gelatin film, this may be explained that the amino group in the network structure of membrane is protonated in the low pH, leading to the increase of electrostatic repulsion and hydrophilicity, therefore the membrane structure becomes loose, and the swelling rate goes up.

Table 3 is pH effect on diffusion coefficient of 0.5% potassium sorbate in gelatin films. It can be seen that the diffusion coefficients of potassium sorbate increase with the decrease of pH. Receiving solution pH values has certain effect on the diffusion process, which is associated with the swelling of the membrane. As shown in Figure 4, the higher the swelling rate of membrane, the larger the channel of membrane, which cause the high mobility of potassium sorbate in pH 3.5.