International Journal of Polymer Science
Volume 2015 (2015), Article ID 176826, 11 pages
http://dx.doi.org/10.1155/2015/176826

Research Article

Prediction of Mold Spoilage for Soy/Polyethylene Composite Fibers

Chinmay Naphade,¹ Inyee Han,² Sam Lukubira,³ Amod Ogale,³ James Rieck,⁴ and Paul Dawson²

¹Farbest Foods, Jasper, IN 47546, USA
²Food, Nutrition and Packaging Sciences, Clemson University, Clemson, SC 29634, USA
³Chemical and Biomolecular Engineering, Clemson University, Clemson, SC 29634, USA
⁴Department of Mathematics, Clemson University, Clemson, SC 29634, USA

Received 1 September 2014; Accepted 19 December 2014

Academic Editor: Long Yu

Copyright © 2015 Chinmay Naphade et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Mold spoilage was determined over 109 days on soy/PE fibers held under controlled temperatures (T) ranging from 10°C to 40°C and water activities from 0.11 to 0.98. Water activities were created in sealed containers using saturated salt solutions and placed in temperature-controlled incubators. Soy/PE fibers that were held at 0.823 or higher exhibited mold growth at all temperatures. As postulated, increased water activity (greater than 0.89) and temperature (higher than 25°C) accelerated mold growth on soy/PE fibers. A slower mold growth was observed on soy/PE fibers that were held at 0.87 and 10°C. A Weibull model was employed to fit the observed logarithmic values of , and an interaction term and was chosen as the final model as it gave the best fit to the raw mold growth data. These growth models predict the expected mold-free storage period of soy/PE fibers when exposed to various environmental temperatures and humidities.

1. Introduction

Natural/biofiber composites are emerging as a viable alternative to glass fiber composites, particularly in automotive, packaging, building, and consumer product industries becoming one of the fastest growing additives for thermoplastics. Biocomposites can mimic the structures of living materials by providing strengthening properties to the matrix while still providing biocompatibility, for example, in creating scaffolds in bone tissue engineering [1] (Kispotta and Bisoyi, 2011). Biocomposites are composite materials that contain one or more phase(s) derived from a biological origin [2]. For biocomposites the reinforcement could be fibers like cotton, flax, hemp, wood, or even by-products from food crops. Matrices may be polymers, ideally derived from renewable resources such as vegetable oils or starches. One of the most commonly used matrices is synthetic, fossil-derived polymers. Biocomposites integrate “soft” biological and organic molecular assemblies with “hard” inorganic nanoarchitectures combining materials having disparate chemical and physical properties within a single system.

The addition of natural fillers or reinforcements is postulated to lower the manufacturing cost and increase the stiffness of composites [3]. Fillers also provide advantages of lower energy consumption and faster cycle time during production. Another major advantage of these reinforcements is incorporation of biopolymers such as starches and proteins into composites enhancing degradation of plastic materials [4].

Several studies have reported on the incorporation of biopolymers, such as starch and protein, into extrusion blown polyethylene films [5, 6]. Films combining protein with synthetic plastics show potential for production of compostable plastic materials. Degradation of proteins by microorganisms can render the remaining synthetic polymer vulnerable to photodegradation or thermal degradation. Gurram et al. (2002) [7] studied the properties of wood, soy hull fiber, and big blue stem on the tensile and flexural properties of fibers. They found that Young’s modulus of wood, big blue stem, and soy hull fiber composites were comparable to pure polypropylene and polyethylene. These researchers also concluded that biorenewable fibers such as soybean hulls could be used as reinforcing materials for low cost composites and that environmental and energy savings benefits could be another advantage of biocomposites. Zhang et al. (1999) [8] studied biocomponent fibers that were wet-spun from soybean protein and poly(vinyl alcohol) for textile applications. They determined that the protein core of the spun biocomponent fiber was brittle and showed a high frequency of core breakage upon drawing. Thus an effort was made to investigate the soybean protein solution, with the aim of trying to understand the cause for fiber brittleness and to determine the optimum solution conditions for fiber spinning.

Ghorpade et al. (1995) [9] evaluated the cast forming ability of soy protein isolates with varying amounts of polyethylene oxides (PEO) and determined that addition of PEO decreased film tensile strength (TS) and increased elongation at break (). Scanning electron micrographs of film cross-sections showed a decrease in positive texture attributes with increasing amounts of PEO in the films. Jong (2005) [10] used defatted soy flour (DSF) for rubber reinforce- ments. The reinforcement mechanism of DSF in rubber used carboxylated polystyrene-butadiene as a composite matrix and was characterized by static and dynamic mechanical methods. These results indicated that DSF was a more effective option than either soy protein isolate or concentrate in terms of both mechanical properties and cost.

The growth of microorganisms like bacteria or molds on a substrate is governed by the intrinsic and extrinsic factors [11, 12]. Following are the important intrinsic factors:

(i)moisture content,(ii)nutrient content,(iii)oxidation-reduction potential (Eh)(iv)pH.

Extrinsic factors influencing microbial growth are

(i)temperature,(ii)relative humidity,(iii)presence and concentration of gases,(iv)presence and activities of other microorganisms.

Mold can grow on many surfaces where oxygen and moisture are present. Biocomposites are more susceptible to microbial growth than fossil-derived polymers due to their hydrophilic nature and nutrient availability. Moisture sorption isotherms have been studied for a range of biological materials including starch powders [13, 14], pasta [15], tea leaves [16], corn stover [17], alfalfa cubes [18], oats/oatmeal biscuits [19], bean flour [20], and cookies [21]. Moisture sorption isotherms have also been used to study bio-based films formed from starch [22], whey protein [23], chicken feather keratin [24], and zein [25]. Models predicting mold growth under various moisture conditions have also been developed [26].

Igathinathane et al. (2008) [27] developed a model to predict the storage life of corn stover components without mold growth when exposed to different temperature and humidity conditions. In order to maintain humidity conditions, saturated salts solutions were placed in temperature controlled chambers. The desiccators were used to create environments having temperatures from 10°C to 40°C and of 0.11 to 0.98. At a high water activity (>0.90 ) and a temperature of 30°C, mold growth occurred in corn leaf, stalk, and skin rapidly. One-, two-, and three-parameter models were assessed for their performance to predict mold-free days (MFDs) based on temperature and . The three-parameter model gave the best prediction compared to the exponential model. The single parameter product model produced slightly better results than the two-parameter model. Three-parameter model featured all parameters and the -statistics revealed that the combined product variable was more significant than variables of and . They concluded that a predictive model could be utilized to predict the safe storage period of corn stover components under controlled temperature and conditions.

Various authors [28–30] reviewed different mathematical isotherm models that can be used to predict the stability of biological materials. Though several articles have been studied, there is no single model identified that can describe the sorption characteristics of soy composites. Thus, the objective of the present study was to develop statistical model to predict mold-free shelf life of soy/PE based as influenced by temperature and water activity.

2. Materials and Methods

2.1. Production of Soy/PE Fibers

Soy flour, grade of 7B2, was provided by ADM (Archer Daniels Midland Company, USA). Linear low density PE, ASPUN grade, was provided by Dow Chemicals (Bristol, Pennsylvania). All fibers were produced at Clemson University Chemical and Biomolecular Engineering. Soy/PE fibers were produced using a proprietary blending of defatted soy flour, a spun pure PE pellets, and a compatibilizer. These materials were blended together using a DSM compounder twin screw microextruder (Xplore Pharma, RD Geleen, Netherlands), to obtain dispersion of soy particles in PE phase. The blended materials were further extruded using a pilot scale single screw extruder (Alex James & Associates, Greenville, SC) to melt spin soy/PE fibers and pure PE fibers. Pellets were fed to single screw extruder that was designed to deliver molten soy/PE mixture at constant pressure to the melting pump. The extruder die had three 500 micron diameter openings to extrude fibers. Fibers were then spun on a continuously spinning unit with a take-up of specific revolutions per minutes (rpm), reducing fiber diameter. This process yielded consistent fibers having a diameter of 50–100 microns, which were further spun on a clean spool.

2.2. Saturated Salt Solutions

Individual containers (16 ounce pint Mason Jars, Ball, Rome, Georgia) were used to hold fiber samples. The various water activities were created by the addition of nine different salts (lithium chloride, potassium acetate, magnesium chloride, potassium carbonate, sodium bromide, sodium chloride, potassium chloride, potassium nitrate, and potassium sulfate) in 70 mL of nanopure water until each solution was saturated. Salts and water solutions were vigorously agitated using magnetic stirrer to facilitate saturation. Additional salt was added as initially added salts dissolved in water to maintain saturation. Saturated salt solutions were placed in temperatures of 10, 25, 30, 35, and 40°C. Once saturated salt solutions became temperature equilibrated, ranging from 0.11 to 0.98 was generated depending upon the salt and temperature combination (Table 1).

Table 1: Water activity of saturated salt solutions at five different temperatures.

Saturated salt solution
Water activity

10°C
25°C
30°C
35°C
40°C

Lithium chloride
0.113
0.113
0.113
0.113
0.112

Potassium acetate
0.234
0.225
0.216
0.216
0.216

Magnesium chloride
0.335
0.328
0.324
0.321
0.316

Potassium carbonate
0.431
0.432
0.432
0.41
0.40

Sodium bromide
0.622
0.576
0.560
0.546
0.532

Sodium chloride
0.757
0.753
0.751
0.749
0.747

Potassium chloride
0.868
0.843
0.836
0.830
0.823

Potassium nitrate
0.960
0.936
0.923
0.908
0.890

Potassium sulfate
0.982
0.973
0.970
0.967
0.964

2.3. Sample Preparation

Soy/PE and pure PE fibers were carefully removed from the spool using sterile gloves as received from production. 1.000 g of fiber was weighed on a digital balance with a sensitivity of 0.0001 g. Fiber samples were prepared from soy/PE fiber spool and stored in a sterile glass holder. Fiber samples were weighed and all necessary information such as initial weight before drying, final weight after drying, and the sample number was marked onto the glass holders. Samples were loaded into a convection oven (Thelco Laboratory Oven 130DM, Precision Scientific, Chicago, Illinois) at 55°C for 15 hrs to equilibrate fiber moisture content to <0.1%. Fibers were then held in a desiccator for 1 hr to cool. Fiber samples were reweighed placed in a sterilized aluminum pans and were randomized using random number generator statistical software [31] (SAS 9.3, 2012).

Initially fiber samples that were predried were placed in nine different salt solution containers (Figure 1) at temperatures of 10, 25, 30, 35, and 40°C (Gravity Convection Incubator 1.1CF120, VWR, Atlanta, GA). Water activities ranged from 0.11 to 0.98 depending upon the salt and temperature combination. Soy/PE fiber samples were placed in all the above-mentioned conditions for 50 days to examine the range of water activity at which mold spoilage was observed on soy/PE fibers. The experiment was run twice independently with a fresh spool of soy/PE fiber for each replication. Fibers that were stored in high (in a range of 0.8–0.98) exhibited mold growth and hence a separate experiment (that was replicated 3 times) was conducted to develop a model that could precisely predict the onset of mold growth in soy/PE fibers.

Figure 1: Experimental setup for establishing different water activities in containers using different saturated salt solutions. One gram of soy/PE fiber sample was placed in each jar in aluminum pans.

2.4. Experimental Setup

30 soy/PE fiber samples placed in the desiccator for 1 hr were reweighed in aluminum pans before they were loaded into saturated salt solution containers. Before loading into saturated salt solution containers, soy/PE fiber samples were randomized as mentioned above in sample preparation. Weighing process was critical and hence was carried out quickly as fibers were dry in nature and long-term exposure to laboratory air could have led to reabsorption of moisture. A one ounce small glass (Anchor Hocking number 82412) was placed into the saturated solution with an aluminum pan containing fiber sample carefully positioned on the glass (Figures 2(a), 2(b), and 2(c)). This arrangement avoided any contact of aluminum pan with the saturated salt solution. Lids were opened daily and the fiber samples were thoroughly inspected for any possible visual signs of mold growth and fiber sample weights were monitored regularly until fibers had attained equilibrium moisture content (EMC). The moisture content of the product in equilibrium with air is known as EMC and the relative humidity of the air as equilibrium relative humidity (ERH) [32]. Crystalline thymol is commonly used in moisture sorption studies as an antimicrobial to prevent microbial spoilage at very high relative humidity and was not used in this study.

Figure 2: One gram of soy/PE fiber sample in aluminum pans that developed mold spoilage. (a) Mold spores, (b) visible mold mycelium when placed in high humidity environments, and (c) mold growth on fibers with an area approximately 5% of total area that was termed as positive mold spoilage for modeling purposes.

Soy/PE fiber samples were stored at five different temperature-controlled incubators (10, 25, 30, 35, and 40°C) (Gravity Convection Incubator 1.1CF120, VWR, Atlanta, GA, USA). At each temperature setting, 6 fiber samples were held in 3 different saturated solutions (KCl, KNO₃, and K₂SO₄) creating ranges of 0.823–0.868, 0.890–0.960, and 0.964–0.982. Each of the 6 fiber samples was placed in separate saturated solution containers to reduce contamination of mold spores from one sample to another.

2.5. Calculations of Mold-Free Days

Mold growth was regularly monitored on fibers by visual examination. Visible spores and subsequent germ tube development from the spores into a radiating system of hyphae known as mycelium (white to greenish cloudy appearance) were an indication of mold spoilage on the fiber surfaces. Fiber surfaces demonstrating equivalent or more than 5% surface area covered with mold (spores or mycelium) were termed as positive for mold spoilage (Figure 2(c)). Without the aid of magnifying lenses, the smallest object humans can resolve approximately 100 μm or 0.1 mm in diameter, which is approximately the size of a fine pencil dot [33]. Therefore, this is the range of mold colony size that could first be observed in this study. Elapsed days until the day of first mold appearance in the form of black dots or visible network of mycelium (Figure 2) was observed and was designated as mold-free days (MFDs) for modeling purposes. Mathematically, MFD is one less than the days counted to the first mold appearance [11]. Moisture absorbed in fibers during experiments was calculated from the initial and final sample weights. Weight gained by soy/PE fibers was monitored regularly. The experiment was replicated 3 times using a fresh spool of soy/PE fiber for each replicate.

2.6. Model Development and Selection

The number of MFDs under specific temperature and water activity conditions can vary from one replicate to another. Thus, MFD is a random variable that has a probability distribution. This probability distribution also affected temperature and for which a model was developed to account for these effects.

In this study, several probability distributions with a location and a scale parameter were considered to represent the distribution of MFDs. These distributions included the normal, lognormal, and Weibull distributions. The regression model assumes that the location parameter is a linear function of independent variables. Candidate independent variables for this study included the temperature (), water activity (), the interaction of temperature and water activity () and the transformations of the logarithm (base 10) of temperature (L), the logarithm of water activity (L) and the interaction of the logarithm of temperature, and the logarithm of water activity (LL).

For all three distributions, the following candidate sets of independent variables were used for the regression model of the location parameter: (), (), (), (, ), (, ), (, ), (, , ), (L), (L), (LL), (L, L), (L, LL), (L, LL), and (L, L, LL). The LIFEREG procedure from SAS was used to obtain the maximum likelihood estimates for the scale parameter and the regression coefficients for all the candidate sets of independent variables.

Model selection criteria such as Akaike information criterion (AIC) and Akaike information criterion correction (AICc) can be used to choose among the various distributions and sets of independent variables. The AIC provides an estimate of the expected Kullback-Leibler information that measures the information loss when the current model is used to approximate the “true” model that generated the data. Thus models with small AIC values are preferred since less information is lost. The AIC is calculated by

where () is the maximized likelihood of a fitted model and () is the number of free parameters in the model itself. When the sample size () is small with respect to the maximum in the set (approximately ), AIC is no longer adequate. A better estimate is provided by AICc which provides a finite sample correction for the Akaike information criterion. The AICc can be calculated by

The statistic of a model in a model set is simply

where is the minimum value of AIC in the set (hence, for the best model). Models with less than approximately 8–12 have essentially no support, those in which 4 ≤ ≤ 7 have considerably less support, models with between 0 and 4 receive considerable support from the current data, and models with in the 0–2 range perform virtually as well as the best model in the set [34].

Burnham and Anderson (2002) [35] strongly recommend using AICc rather than AIC, if is small or is large. For this study, the AICc was calculated for each candidate distribution and set of independent variables. In addition, pseudo for the models was estimated using the likelihood ratio [36]. The pseudo -squared is calculated as follows:

where is pseudo -squared value, Likelihood (model with no independent variables), Likelihood (current model), and is sample size.

The predicted values of MFDs from the chosen model were obtained for the all the temperatures (ranging from 10°C to 40°C) and (ranging 0.80 to 1.00). A 3D surface plot was developed for predicted MFD values for (0.80–1.00) and temperature (10°C–40°C) using MATLAB software (R2012B, The MathWorks, Natick, MS). The observed values of MFDs from all three replications were then mapped on the 3D surface model from all replications to establish the prediction efficacy of the best chosen model. A precise mapping of the observed values of MFDs on the 3D surface suggests prediction capability of the optimal model superior to that of the other chosen models.

3. Results and Discussion

Soy/PE fibers placed in environments ranging from 0.112 to 0.982 at five different temperatures (10°C, 25°C, 30°C, 35°C, and 40°C) for 50 days developed mold growth only at the higher (0.8–0.98) levels. Hence a separate experiment was implemented to determine a best suited model using SAS 9.3 and develop a 3D plot using MATLAB software to predict mold growth on fibers exposed to temperature and humidity conditions under which mold growth developed after 50 days.

Soy/PE fibers held with saturated potassium chloride solutions (0.868–0.823 ) absorbed the least moisture (in a range of 0.0329–0.0631 g) (Figure 3) and hence a slower mold growth in fibers was observed. For fiber samples held with potassium chloride solutions (0.868 ), ones held at 10°C had the greatest MFDs (101–108) compared to fibers held under other temperatures. Fibers held with potassium chloride solutions (0.868–0.823 ) at 25°C, 30°C, 35°C, and 40°C had MFDs in a range of 38–52 (Table 2).

Table 2: Mold-free days (MFD) for soy/PE fiber samples held at different temperatures and water activities.

Temperature
() in °C
Water
activity ()
Replication 1
Replication 2
Replication 3
Average

MFD
Final moisture
content
MFD
Final moisture
content
MFD
Final moisture
content
MFD

10
0.868
105
0.055
101
0.0631
99
0.0566
102
8.68

0.868
106
0.0578
108
0.0596
102
0.0589
105
8.68

0.96
40
0.1212
40
0.1473
38
0.1346
39
9.6

0.96
40
0.1248
39
0.1423
39
0.1295
39
9.6

0.982
34
0.2258
32
0.2329
32
0.2322
33
9.82

0.982
33
0.2302
33
0.237
32
0.2275
33
9.82

25
0.843
52
0.0461
49
0.0578
49
0.0529
50
21.08

0.843
51
0.0457
49
0.0573
50
0.0499
50
21.08

0.936
13
0.0742
13
0.0857
14
0.0777
13
23.40

0.936
12
0.0752
14
0.081
13
0.0789
13
23.40

0.973
10
0.1896
9
0.2192
8
0.2008
9
24.33

0.973
9
0.1956
9
0.2218
9
0.1945
9
24.33

30
0.836
49
0.0451
45
0.0533
43
0.047
46
25.08

0.836
48
0.044
45
0.0529
42
0.0468
45
25.08

0.923
10
0.0717
12
0.0775
11
0.0748
11
27.69

0.923
9
0.0721
12
0.0783
12
0.0739
11
27.69

0.97
8
0.1701
8
0.1879
8
0.1763
8
29.10

0.97
8
0.1682
8
0.1905
8
0.1734
8
29.10

35
0.83
44
0.0401
43
0.0465
40
0.0392
42
29.05

0.83
43
0.039
42
0.0489
40
0.0382
42
29.05

0.908
8
0.0672
10
0.0724
10
0.0678
9
31.78

0.908
8
0.0652
10
0.071
11
0.0673
10
31.78

0.967
7
0.1627
7
0.1697
6
0.162
7
33.85

0.967
7
0.1629
6
0.1742
6
0.1665
6
33.85

40
0.823
41
0.0378
40
0.0421
38
0.0347
40
32.92

0.823
41
0.0381
40
0.0412
38
0.0329
40
32.92

0.89
6
0.0642
7
0.0688
7
0.0594
7
35.60

0.89
7
0.0606
7
0.0659
7
0.062
7
35.60

0.964
5
0.1618
4
0.1657
5
0.1572
5
38.56

0.964
5
0.1611
5
0.1646
5
0.1564
5
38.56

Figure 3: Soy/PE fiber samples stored with potassium chloride salt solutions at different temperatures (10°C, 25°C, 30°C, 35°C, and 40°C). Ultimate moisture absorbed during storage in different (0.868, 0.846, 0.836, 0.830, and 0.823, respectively). Each data point denotes a mean value of 6 samples in 3 replications.

Soy/PE fibers held with potassium nitrate solutions (0.890–0.960 ) absorbed moisture in a range of 0.0594–0.1473 g (Figure 4). Soy/PE fibers held at 0.960 and 10°C had MFDs of 38–40, while fibers held with potassium nitrate solutions (0.890–0.936 ) and kept at 25, 30, 35, and 40°C had MFDs in a range of 6–14 (Table 2).

Figure 4: Soy/PE fiber samples stored with potassium nitrate salt solutions at different temperatures (10°C, 25°C, 30°C, 35°C, and 40°C). Ultimate moisture absorbed during storage in different relative humidities (0.960, 0.936, 0.923, 0.908, and 0.890, respectively). Each data point denotes a mean value of 6 samples in 3 replications.

Soy/PE fiber samples held with potassium sulfate solutions (0.964–0.982 ) absorbed moisture in the range of 0.1564–0.237 g (Figure 5). The potassium sulfate solution yielded the highest water activity 0.982 at 10°C resulting in MFDs of 32–34, while fibers held with the same salt solution at 25, 30, 35, and 40°C with 0.964–0.973 had MFDs in a range of 4–10 (Table 2). Thus, soy/PE fibers were comparatively less stable to mold growth and can display mold growth before 10 days when temperatures are ≥25°C and ≤40°C and is in a range of 0.964–0.973. Fibers did not have mold growth for 3 days under the most extreme (high temperature, high ) conditions tested (Figure 6).

Figure 5: Soy/PE fiber samples stored with potassium sulfate salt solutions at different temperatures (10°C, 25°C, 30°C, 35°C, and 40°C). Ultimate moisture absorbed during storage in different relative humidities (0.982, 0.973, 0.970, 0.967, and 0.964, respectively). Each data point denotes a mean value of 6 samples in 3 replications.

(a)

(b)

Figure 6: (a) Prediction model for the median number of mold-free days (MFDs) based on temperature () and water activity () values obtained from the Weibull distribution utilizing observed logarithmic values of , , and an interaction term of of three replications. Observed mold growth expressed as mold-free days (MFDs) on soy/PE fiber samples from all three replications shown as points on the graph to demonstrate the relationship of observed values to the predicted values. (b) A side-view of (a).

Fiber samples stored at all and placed in 25, 30, 35, and 40°C incubators absorbed maximum moisture within 2 days and subsequently a slight increase or retention of moisture was observed over the time of study. A gradual increase in moisture content was observed in fiber samples stored at all at 10°C. However, fiber samples stored in highest (0.964–0.982) and placed in 25, 30, 35, and 40°C initially absorbed more moisture as compared to fibers stored at 10°C. Hence, it may be concluded that temperature and rate of moisture absorption accelerated mold growth in soy/PE fibers kept at 25, 30, 35, and 40°C compared to 10°C. Temperature also affects the growth rate with the optimum growth temperature between 30 and 40°C.

For the first replicate, the three models that possessed the smallest AICc values for the Weibull distribution were the (L, L), (L, LL), and (L, L, LL) models (Table 3). The AICc values were 175.654, 172.341, and 173.439, respectively. Since the difference in the AICc values among the three models was less than 3 there is no preference among these models. For the second replicate, the three models that possessed the smallest AICc values for the Weibull distribution were again the (L, L), (L, LL), and (L, L, LL) models (Table 3). The AICc values were 160.645, 155.6, and 155.235, respectively. Since the difference in the AICc values for the (L, L) model is over 5 compared to the other two models, it was not chosen as a preferred model. There was no preference between the (L, LL) and the (L, L, LL) models. For the third replicate, the three models that possessed the smallest AICc values for the Weibull distribution continued to be the (L, L), (L, LL), and (L, L, LL) models (Table 3). The AICc values were 131.432, 132.69, and 132.079, respectively. Since the difference in the AICc values for the (L, L), (L, LL), and the (L, L, LL) models is the same, there was no preference between the (L, L), (L, LL), and the (L, L, LL) models.

Table 3: LIFEREG procedure analysis in SAS 9.3 using lognormal and Weibull distribution utilizing observed logarithmic values of , , and a logarithmic interaction term of and MFD in three individual replications.

Distribution

Model
AICc

Pseudo -squared

Values from Experiment 1

Lognormal
30
LL
256.404
249.481
0.226

Lognormal
30
L, L
187.678
178.078
0.929

Lognormal
30
L, LL
186.637
177.037
0.931

Lognormal
30
L, LL
233.236
223.636
0.673

Lognormal
30
L, L, LL
188.727
176.227
0.933

Lognormal
30
None
261.616
257.171
0

Weibull
30
LL
263.024
256.101
0.140

Weibull
30
L, L
175.654
166.054
0.957

Weibull
30
L, LL
172.341
162.741
0.962

Weibull
30
L, LL
240.402
230.802
0.630

Weibull
30
L, L, LL
173.439
160.939
0.964

Weibull
30
None
265.086
260.641
0

Values from Experiment 2

Lognormal
30
LL
254.99
248.067
0.215

Lognormal
30
L, L
173.822
164.222
0.961

Lognormal
30
L, LL
172.053
162.453
0.953

Lognormal
30
L, LL
230.366
220.766
0.784

Lognormal
30
L, L, LL
173.648
161.148
0.961

Lognormal
30
None
260.7
256.256
0

Weibull
30
LL
262.011
255.088
0.119

Weibull
30
L, L
160.645
151.045
0.979

Weibull
30
L, LL
155.6
146
0.974

Weibull
30
L, LL
237.922
228.322
0.758

Weibull
30
L, L, LL
155.235
142.735
0.979

Weibull
30
None
263.902
259.458
0

Values from Experiment 3

Lognormal
30
LL
235.626
228.703
0.230

Lognormal
30
L, L
148.411
138.811
0.962

Lognormal
30
L, LL
152.244
142.644
0.956

Lognormal
30
L, LL
201.617
192.017
0.773

Lognormal
30
L, L, LL
151.25
138.75
0.962

Lognormal
30
None
241
236.556
0

Weibull
30
LL
243.242
236.319
0.135

Weibull
30
L, L
131.432
121.832
0.981

Weibull
30
L, LL
132.69
123.09
0.980

Weibull
30
L, LL
211.692
202.092
0.724

Weibull
30
L, L, LL
132.079
119.579
0.982

Weibull
30
None
245.123
240.679
0

The three replications were successfully converged into one and the three models that possessed the smallest AICc values for the Weibull distribution were the (L, L), (L, LL), and (L, L, LL) models. The AICc values were 454.527, 447.77, and 441.685, respectively. The model (L, L, LL) was the best suited model among the chosen sets and was determined based on the least AICc number and highest pseudo value (0.974) (Table 4). for the (L, L, LL) model would be zero. Since the for the (L, L) model is over 12 compared to (L, L, LL) model and for the (L, LL) model is over 6 compared to (L, L, LL) model, those models were not chosen as preferred models.

Table 4: LIFEREG procedure analysis in SAS 9.3 using normal, lognormal, and Weibull distribution utilizing observed logarithmic values of , , and a logarithmic interaction term of and MFD by converging all three replications together.

Distribution

Model
AICc

Pseudo -squared

Normal
90

795.929
789.65
0.304

Normal
90

777.768
771.489
0.431

Normal
90

794.574
788.295
0.315

Normal
90

722.94
714.47
0.698

Normal
90

641.592
630.877
0.881

Normal
90

664.946
656.476
0.842

Normal
90

675.076
666.606
0.823

Normal
90
None
826.443
822.305
0

Lognormal
90

721.653
715.374
0.319

Lognormal
90

696.565
690.286
0.485

Lognormal
90

714.953
708.674
0.368

Lognormal
90

513.004
504.533
0.935

Lognormal
90

501.898
491.183
0.944

Lognormal
90

534.015
525.544
0.918

Lognormal
90

503.76
495.289
0.941

Lognormal
90
None
754.145
750.007
0

Lognormal
90
L
720.065
713.786
0.331

Lognormal
90
LL
732.591
726.312
0.231

Lognormal
90
L
714.13
707.851
0.374

Lognormal
90
L, LL
649.852
641.381
0.701

Lognormal
90
L, L, LL
491.783
481.069
0.949

Lognormal
90
L, LL
494.044
485.574
0.947

Lognormal
90
L, L
494.084
485.613
0.947

Lognormal
90
None
754.145
750.007
0

Weibull
90
L
737.865
731.586
0.278

Weibull
90
LL
753.965
747.686
0.137

Weibull
90
L
735.125
728.846
0.299

Weibull
90
L, LL
672.841
664.371
0.658

Weibull
90
LT, LA, LTLA
441.685
430.971
0.974

Weibull
90
L, L
454.527
446.057
0.969

Weibull
90
L, LL
447.77
439.299
0.972

Weibull
90
None
765.045
760.907
0

Thus the (L, L, LL) model was a preferred model for all three replicates and the final converged replicate and hence it was chosen as the final model. The data from all three replicates were pooled and each replicate was treated as a random effect for the location parameter and the final maximum likelihood estimates for the scale and location parameters were determined using the NLMIXED procedure from SAS 9.3 (SAS, 2012). The maximum likelihood estimate of the scale parameter is given by

The maximum likelihood estimate for the location parameter is given by the following equation:

The maximum likelihood estimate of the percentile of mold-free days is given by

For example, to estimate the median number of mold-free days, is 0.5.

The pseudo -squared for the model is 0.974 (Table 4).

A 3D surface was developed using values obtained from converged replications (i.e. predicted values of MFDs for an entire set of temperatures (10°C–40°C) and water activity (0.80–1.00)) (Figures 6(a) and 6(b)). The observed MFD values from all the three replications were then mapped on the 3D surface of the model derived from all replications. These MFD values appeared on the 3D surface plot with no or very little deviation for the model (Figure 6(b)). It was concluded that the selected model was effective for predicting MFDs at given temperatures (10°C–40°C) and (0.80–1.00 ) (Figures 6(a) and 6(b)). Mold growth on biocomposite films is more likely compared to petroleum-based films due to the availability of nutrients and moisture. Iganthinathane et al. (2008) [27] modeled the MFDs to predict the safe storage time and conditions for corn stover reporting that the product of storage temperature and storage was simple predictor of mold-free days. This only held for the present study for similar at different temperatures (Table 2). When a greater number of temperatures and were tested, predicting the growth of mold was not as straightforward. The current study demonstrates a method to predict mold growth and permit the safe storage of soy-PE composites. The current model predicts over 200 MFDs when stored at 80% RH (0.8 ) and 10°C. Similar models could be used to predict MFDs for the bio-based fibers to create safe storage periods and conditions for biocomposites.

Films combining protein with synthetic plastics show potential for production of compostable plastic materials. In particular, nonwoven products are replacing many woven and knit materials because they are low in cost and are lightweight. Degradation of bio-based components by microorganisms can render the remaining synthetic polymer vulnerable to photodegradation or thermal degradation. While the use of biocomposites can be expanded to produce highly functional, inexpensive material, the need for testing to determine stability will be required due to the degradability of the biological component. The methods and results reported here predict the stability bio-based composites and can be used to develop stable biocomposites in the future.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment

This research was partially supported by a Grant from the United Soybean Board (USB), Grant no. 1480 and 9480 “Continuous Calendering-Extrusion Route: Melt-Processing of Ribbon-Fiber Based Nonwovens and Films Derived from Soy Proteins.”

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