Patent Publication Number: US-11390571-B2

Title: PAMAM dendrimers for fertilizer delivery

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to and the benefit of U.S. Provisional Patent Application No. 62/787,793, filed on Jan. 3, 2019, which is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND OF THE DISCLOSURE 
     Agricultural fertilizers or other agents are delivered to plants in a variety of methods. The fertilizer is delivered either to the root structure of the plant or through the leaves of the plant where the fertilizer is taken up through pores in the leaves—including cuticular cracks/pores. Additionally, the fertilizer is applied to the soil or leaves in a dry form or mixed in a fluid medium to suspend the fertilizer and mobilize the fertilizer. 
     Conventionally, the fluid application of the fertilizer or other agent can allow for more even and controlled application, as well as more rapid uptake of the fertilizer or other agent. Foliar application (application of a fertilizer to the leaves of the plant) can provide a more direct application of the fertilizer to the plant. 
     SUMMARY 
     In some embodiments, an agricultural formulation for conveying nutrients to a plant includes Poly(aminoamide) (PAMAM) dendrimers and a fertilizer active ingredient. 
     In some embodiments, an agricultural fertilizer formulation includes a liquid medium, a fertilizer active ingredient, and PAMAM dendrimers. The liquid medium and fertilizer active ingredient define a total volume. A volume ratio of the PAMAM dendrimers to the total volume of the liquid medium and fertilizer active ingredient is at least 1 parts per billion. 
     In some embodiments, a method of administering a fertilizer to a plant includes providing a fluid fertilizer mixture including fertilizer and a liquid medium having a volume ratio between 1:160 and 1:32,000, adding PAMAM dendrimer to the fluid fertilizer mixture to create a formulation where the dendrimer mass to fertilizer volume ratio is between 3 parts per million and 10 parts per million, and applying the formulation to the plant. 
     This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter. 
     Additional features and advantages of implementations of the disclosure will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of such implementations. The features and advantages of such implementations may be realized and obtained by means of the instruments and combinations particularly pointed out in the appended claims. These and other features will become more fully apparent from the following description and appended claims or may be learned by the practice of such implementations as set forth hereinafter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In order to describe the manner in which the above-recited and other features of the disclosure can be obtained, a more particular description will be rendered by reference to specific implementations thereof which are illustrated in the appended drawings. For better understanding, the like elements have been designated by like reference numbers throughout the various accompanying figures. While some of the drawings may be schematic or exaggerated representations of concepts, at least some of the drawings may be drawn to scale. Understanding that the drawings depict some example implementations, the implementations will be described and explained with additional specificity and detail through the use of the accompanying drawings in which: 
         FIG. 1  is a schematic representation of foliar application of a fertilizer formulation from a spray truck to the leaves of a plant, according to at least one embodiment of the present disclosure; 
         FIG. 2  is an illustration of the chemical structure of a PAMAM dendrimer, according to at least one embodiment of the present disclosure; 
         FIG. 3  is a graph illustrating the performance of foliar fertilization in hops using PAMAM dendrimers, according to at least one embodiment of the present disclosure; 
         FIG. 4  is a graph illustrating yields of wheat using different fertilization methods, according to at least one embodiment of the present disclosure; 
         FIG. 5  is a graph illustrating potassium concentrations in watermelons using different fertilization methods, according to at least one embodiment of the present disclosure; 
         FIG. 6  is a graph illustrating nitrogen concentrations in millet after only PAMAM dendrimer applications, according to at least one embodiment of the present disclosure; and 
         FIG. 7  is a graph illustrating yield increases in wheat after only PAMAM dendrimer applications, according to at least one embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     This disclosure generally relates to devices, systems, and methods for increasing the uptake of fertilizer in a plant. More particularly, the present disclosure relates to systems, mixtures, and methods for increasing the efficiency of foliar application of a fertilizer to a plant. In at least one embodiment of the present disclosure, a mixture of fertilizer and Poly(aminoamide) (PAMAM) dendrimers is applied to the leaves of a plant. In comparison to a conventional fertilizer mixture, a greater proportion of applied fertilizer is taken up by the leaves of a plant when the mixture includes PAMAM dendrimers with the fertilizer in a fluid medium. 
     Foliar feeding is the direct application of a mixture including a fertilizer or other agricultural agent directly to the leaves of a plant. Plants are able to absorb at least portions of the mixture through the stomata and the epidermis of the leaves. In some cases, the transport to nutrients may be faster through the stomata, but the overall absorption through the epidermis may result in a greater volume of nutrients absorbed. The different transport rates of the different parts of the leaf may result in a broader absorption curve of the nutrients as an initial dosage is received through the stomata and longer duration absorption occurs through the epidermis. 
     Foliar fertilization has been shown to produce a faster response than soil-based fertilization, as the fertilizer is absorbed directly into the leaves. Additionally, soil-based application can result in a leaching-out of the soil. For example, phosphorus applied to the soil can become fixed in a form that is inaccessible to the plant, thereby limiting the overall proportion of the nutrient taken up by the plant. In contrast, the fertilizers and other agents (collectively agrochemicals) applied to the leaves of a plant will not interact with other materials or other organisms in the soil. 
     However, there is a chance that the agrochemicals applied to the leaves are not absorbed. In some cases, the agrochemicals are shed from the leaves. In other cases, the agrochemicals simply dry on the leaves and are not absorbed. Availability of the fertilizer or other agents can include tailoring of the mixture to the plant, the environment, and the delivery mechanism. For example, proper adjustment of the mixture and the system can improve biological efficacy with a lower application rate and/or amount, as well as a lower impact on the environment and lower cost. Some factors in determining the mixture and application systems include even distribution of the agrochemical over the surface of the plant, safety of the mixture and application for workers and equipment, ease of preparation, performance, and environmental effect. 
     For example, the agrochemicals are applied to the plant in a liquid medium. The preferred liquid medium is water for many agrochemicals. Water may be desirable as a fluid medium for the agrochemicals because water has limited environmental effects and limited safety concerns relative to other options. Additionally, many crop plants require supplemental watering, and application of agrochemicals during watering can save time, resources, and money. 
     Various agrochemical formulations can be used for different purposes and applications. Formulations include an active ingredient and other ingredients such as surfactants, carriers, excipients, or other functional ingredients. For example, the present application will primarily refer to the use of fertilizer with PAMAM dendrimers as a carrier, however, additional ingredients may be used. For example, a fertilizer mixed with PAMAM dendrimers in water may have a greater transport rate than the same fertilizer mixed in water. However, a foliar application of either combination may not sufficiently adhere to the leaves of a plant to provide enough time for the leaves to absorb the active ingredient. In such examples, an additional ingredient may increase the surface tension of the fluid. In other examples, a surfactant may be included to decrease the surface tension. 
     In some embodiments, PAMAM dendrimers have an amine terminal group. The amine group has additional nitrogen atoms that are covalently bonded. As most plants are able to sever the nitrogen-bonds in the amine group, the PAMAM dendrimers are able to additionally deliver usable nitrogen to the plants, in addition to the active ingredients mobilized by the dendrimers in the formulation. The nitrogen in other layers of the dendrimer is also accessible to the plant as the dendrimer layers break down. 
     Environmental volatility may be improved by the nitrogen delivery through larger particles. For example, conventional nitrogen supplements including ammonia, nitrates, or other nitrogen-rich compounds can volatilize during delivery, resulting in a loss of the supplement before or after reaching the plant. Additionally, in some instances, the volatilized nitrogen compounds can be hazardous. For example, nitrates can react energetically in exposure to heat, creating a risk of fire or explosion. The amine terminal groups of a PAMAM dendrimer allow for the delivery of nitrogen to a plant with a lessened risk of volatility. 
       FIG. 1  is a schematic representation of foliar fertilization. A delivery system  100  is used to apply a fluid to the leaves  102  of the plant. In some embodiments, the delivery system  100  is a mobile system, such as a backpack, truck, tractor, trailer, sprayer (boom or row-crop sprayer), or other agricultural machinery that may be loaded with a holding tank  104  and driven to the delivery location. In other embodiments, the delivery system  100  is a stationary system. For example, the delivery system  100  can include a drip irrigation system, such as one using micro spray heads to atomize the formulation. In other examples, the delivery system  100  can include a sprinkler system or a center pivot irrigation system that sprays a liquid formulation onto the surface of the leaves  102 . 
     In a particular example, the delivery system  100  includes a sprayer vehicle with a holding tank  104  and a boom  106 . In such examples, the boom  106  is directed toward the leaves  102  of the plant and a spray  108  of the formulation is delivered to the leaves  102 . In some cases, the formulation may be internally agitated in the holding tank  104  to limit and/or prevent aggregation of the agents in the formulation. In other cases, the formulation may experience external agitation of the movement of the holding tank  104  only, with no further internal agitation. In yet other examples, such as a stationary delivery system, the holding tank may be substantially still with no internal or external agitation. 
     Nanoparticles, as described herein, are particles having a particle diameter between 1 and 1000 nanometers (nm). Nanoparticles tend to have strong surface interactions and aggregate with one another and other particles. Dendrimers, in particular, have a strong tendency to aggregate. 
     Applications of dendrimers conventionally involve conjugating other chemicals to the dendrimer surface that can function as detecting agents (such as a dye molecule), affinity ligands, targeting components, radioligands, imaging agents, or pharmaceutically active compounds. Dendrimers have very strong potential for these applications because their structure can lead to multivalent systems. For example, one dendrimer molecule can have hundreds of possible sites to couple to an active ingredient or chemical agent, depending on the number of generations of branching layers in the dendrimer. 
     Dendrimers are conventionally used for drug delivery applications due to their monodispersity, water solubility, encapsulation ability, and large number of active terminal groups.  FIG. 2  is a structural diagram of an example PAMAM dendrimer  110 . The PAMAM dendrimer  110  has a core  112 . In some examples, the core  112  is a diamine, such as ethylenediamine, that is the basis from which branching layers  114 - 1 ,  114 - 2 ,  114 - 3  or shells or generations are attached. For example, a third generation (3G) dendrimer has three branching layers  114 - 1 ,  114 - 2 ,  114 - 3 . While the branching layers  114 - 1 ,  114 - 2 ,  114 - 3  of the embodiment illustrated in  FIG. 2  repeat, the branching layers  114 - 1 ,  114 - 2 ,  114 - 3  are synthesized sequentially, allowing for different structures in the individual branching layers  114 - 1 ,  114 - 2 ,  114 - 3  if desired. 
     The branching layers  114 - 1 ,  114 - 2 ,  114 - 3  introduce additional terminal sites at each layer, increasing the ultimate number of terminal groups  116  possible with each successive layer. For example, the core  112  has four terminal sites, to which the first branching layer  114 - 1  is connected. The first branching layer  114 - 1  then doubles the number of terminal sites. The second branching layer  114 - 2  and third branching layer  114 - 3  each double the number, as well. In other embodiments, the branching layers  114 - 1 ,  114 - 2 ,  114 - 3  have other multiplicities that change the number of active terminal sites to which the successive generation bonds. For example, each of the branching layers  114 - 1 ,  114 - 2 ,  114 - 3  of the embodiment illustrated in  FIG. 2  has a multiplicity of 2, resulting in 16 terminal groups  116  in the third branching layer. In another example with the same core  112  where each of the branching layers  114 - 1 ,  114 - 2 ,  114 - 3  has a multiplicity of three, the third generation would allow for 48 terminal groups  116 . 
     In some embodiments, the PAMAM dendrimers used to deliver fertilizer and provide supplemental nitrogen are at least second-generation (2G) dendrimers. In other embodiments, the PAMAM dendrimers used to deliver fertilizer and provide supplemental nitrogen are at least 2.5G dendrimers. In yet other embodiments, the PAMAM dendrimers used to deliver fertilizer and provide supplemental nitrogen are at least 3G dendrimers. In further embodiments, the PAMAM dendrimers used to deliver fertilizer and provide supplemental nitrogen are at least 3.5G dendrimers. 
     Fertilizers carry an industry shorthand for the three most common nutrients provided to the plant. The format for the shorthand is generally N—P—K, where the letters are the atomic symbol for the nutrient. For example, a general-purpose fertilizer with a 10-10-10 designation contains 10% by weight of each of a nitrogen-supplying compound, a phosphorus-supplying compound, and a potassium-supplying compound. The remaining composition of the fertilizer is inert ingredients in the formulation. The nutrient-supplying compounds can have net negative or positive charges. 
     During testing, PAMAM dendrimers have shown the ability to mechanically interact with fertilizers to increase the transport of the fertilizer molecule, despite the terminal groups and the fertilizer molecules both being negatively charged. For example, a fertilizer mixture of 12-0-0 Urea with 6% Iron and 3% Manganese concentrations has a net negative charge. While the charge may aid in solubility of the fertilizer mixture, the charge would be expected to inhibit interaction with the PAMAM dendrimers. However, in testing, the PAMAM dendrimers have been shown to increase the mobility of the fertilizer mixture in foliar application. 
     Table 1 includes the results of a test conducted with foliar application of fertilizer formulations on Bermudagrass. Different formulations were applied to seven plots. The response to applied fertilizer formulations was measured in an average greenness rating of the individual plots. All treatments were applied at a rate of 0.1 lb of Nitrogen per 1000 square feet. A tenth of a pound of Nitrogen from this product is 32 ml of fertilizer solution. All treatments were sprayed in a tank with 3.8 L of water. Treatment 1 is a blend of 12-0-0 Urea with 6% Iron and 3% Manganese fertilizer with hollow mesoporous silica nanoparticles having a 120 nm diameter. The hollow mesoporous silica nanoparticles were provided in a concentration of 0.034 mg/ml of fertilizer solution. Treatment 2 is a blend of the fertilizer with hollow iron oxide nanoparticles having a 7 nm diameter. The hollow iron oxide nanoparticles were provided in a concentration of 0.02 mg/ml of fertilizer solution. Treatment 3 is a blend of the fertilizer with G3.5 PAMAM dendrimers at a dendrimer mass to fertilizer volume ratio of 3 parts per million (ppm) concentration. Treatment 4 is a blend of the fertilizer with G3.5 PAMAM dendrimers at a 6 ppm concentration. Treatment 5 is a blend of the fertilizer with a first mixture of spherical nanoparticles having a varied diameter. The nanoparticles were provided in a concentration of 0.007 mg/ml of fertilizer solution. Treatment 6 is a blend of the fertilizer with a second mixture of spherical nanoparticles having a varied diameter. The nanoparticles were provided in a concentration of 0.01 mg/ml of fertilizer solution. Treatment 7 is the control with only the liquid fertilizer solution. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Treat. 
                 Rep A 
                 Rep B 
                 Avg. 
                 Rep A 
                 Rep B 
                 Avg 
                 Rep A 
                 Rep B 
                 Avg 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 6 
                 8 
                 7.0 
                 6 
                 8 
                 7.0 
                 6 
                 7.5 
                 6.75 
               
               
                 2 
                 7 
                 7 
                 7.0 
                 7 
                 7 
                 7.0 
                 7 
                 6 
                 6.5 
               
               
                 3 
                 7 
                 5 
                 6.0 
                 7 
                 5 
                 6.0 
                 6 
                 5 
                 5.5 
               
               
                 4 
                 8 
                 8 
                 8.0 
                 8 
                 8 
                 8.0 
                 7 
                 7.5 
                 7.25 
               
               
                 5 
                 7 
                 7 
                 7.0 
                 8 
                 8 
                 8.0 
                 8 
                 8 
                 8.0 
               
               
                 6 
                 5 
                 8 
                 6.5 
                 5 
                 8 
                 6.5 
                 5 
                 8 
                 6.5 
               
               
                 7 
                 6 
                 7 
                 6.S 
                 6 
                 7 
                 6.5 
                 6 
                 6.5 
                 6.25 
               
               
                   
               
            
           
         
       
     
     Each treatment was applied to two plots (Rep A and Rep B) and measured at three times. The sets of measurements were collected after three days, after 5 days, and after 9 days, respectively. The experiment illustrated that PAMAM dendrimer concentrations above 3 ppm show improved uptake of fertilizer. For example, treatment 4 including the G3.5 PAMAM dendrimers at a 6 ppm concentration represented the fastest absorption and response to the application of the fertilizer with the highest greenness on day 3 and day 5, while the first mixture of spherical nanoparticles (Treatment 5) showed similar improvements in uptake, but did so more slowly. Both the spherical and dendrimer nanoparticles showed an increase in average greenness. The 6 ppm concentration PAMAM dendrimers showed the greatest increase and the fastest increase in greenness. 
     Further tests were conducted on hops, wheat, millet, and watermelons to test both the additional mobility of fertilizers used in conjunction with the dendrimer agent, as well as test the availability of the nitrogen in the PAMAM dendrimers to the plants. Application of the PAMAM dendrimer agent without fertilizer allows the evaluation of the plant&#39;s ability to access the nitrogen in the terminal amine groups independently of any growth or greenness improvements due to a separate fertilizer. While the PAMAM dendrimers described herein show an improvement in crop growth independently, for clarity, the fertilizer is referred to as the active ingredient and the PAMAM dendrimers will be continued to be referred to as a mobilization aid in the formulation. 
     The concentration of the dendrimers in the formulation relative to the concentration of the active ingredient and the relative to the overall volume of fluid into which the dendrimers are added affects the performance. While the dendrimers are able to interact with the active ingredients, the dendrimers also exhibit interaction with the other dendrimers. Therefore, increasing a dendrimer concentration in a constant volume of fluid reduces the performance of the formulation, as the dendrimers aggregate. 
       FIG. 3  through  FIG. 5  illustrate tests demonstrating the additional fertilization provided by the PAMAM dendrimers of the present description. The PAMAM dendrimers are able to increase the transport rate of the applied fertilizer and reduce the amount of fertilizer necessary to produce equivalent or improved yields in both large-scale and small-scale tests. 
       FIG. 3  is an example of the foliar application of two formulations of fertilizer with PAMAM dendrimers in comparison to a conventional application of fertilizer. The regular program in the right bar  120  of the graph  118  is a control application of fertilizer. The bar  124  on the left is a fertilizer formulation including a nanoprepared potash and delivered in a foliar application. As used herein, “nanoprepared” should be understood to mean prepared or produces such that an average particle size of the produce is less than 1 micron. For example, the potash in the “NanoK” product is a potassium supplement (0-0-21) of K 2 O particles with an average particle size of less than 1 micron. The left bar  124  of the graph illustrates a reduction in the regular fertilizer in the formulation of 50% with an introduction of PAMAM dendrimers to the formulation. As shown in the graph  118 , the formulation of the left bar  124  outperformed the regular program of the right bar  120  using half of the fertilizer when PAMAM dendrimers are included in the formulation. 
     The regular program includes a foliar application of a conventional fertilizer for hops. The left bar  124  of the graph  118  reflects a more efficient transport of the fertilizer and the potassium supplement to the plant through the leaves. Additionally, the PAMAM dendrimers of the formulation reflected by the left bar  124  provide nitrogen to the plant. The formulation, therefore, provides a more efficient transport of the fertilizer, while also providing a potassium and nitrogen supplement. 
       FIG. 4  is a chart  226  illustrating the difference in yield from a greenhouse trial of wheat. The regular fertilizer application, both in low concentration illustrated in the second bar  228  and in high concentration illustrated in the third bar  230 , inhibited growth. This may have been due to the fertilizer concentration being too high in salt and retarding growth. The inclusion of dendrimers in the formulation with the low and high concentrations of the fertilizer is illustrated in the fourth bar  232  and fifth bar  234 , respectively. For each of the low concentration and the high concentration, the amount of fertilizer in the application remained the same. For example, the increase between the second bar  228  and fourth bar  232  reflects a change in the low concentration formulation of only the addition of PAMAM dendrimers. Similarly, the increase between the third bar  230  and fifth bar  234  reflects a change in the high concentration formulation of only the addition of PAMAM dendrimers. 
     Finally, the foliar application of only PAMAM dendrimers is reflected in the first bar  236  of the chart  226 . The application of only PAMAM dendrimers resulted in a net increase above the no-treatment control (NTC) bar  238 . The wheat is able to take up the available nitrogen from the PAMAM dendrimers, allowing the PAMAM dendrimers to act as both the transport enhancer and a nitrogen supplement. Testing of the nitrogen uptake of the available nitrogen in the PAMAM dendrimers is described more in relation to  FIG. 6  and  FIG. 7 . 
       FIG. 5  is a graph  340  that illustrates the application of different fertilizer formulations on watermelon crop plants. The graph  340  illustrates a comparison of both root and foliar feeding, as well as dendrimer and non-dendrimer formulations. The graph shows the potassium concentration found in the watermelons produced through the feeding. The first bar  342  reflects the potassium concentration with a regular fertilizer with a conventional potassium supplement at 63 parts per million delivered through a root saturation feeding. The second bar  344  reflects a reduction in the potassium concentration when the same regular formulation with a conventional potassium supplement at 63 parts per million is delivered in a foliar application. Note the offset of the y-axis scale. The foliar application yielded approximately an 8.5% reduction relative to the root application of the regular fertilizer and conventional potassium supplement. 
     The third bar  346  and fourth bar  348  show the effect of nanoprepared potassium supplement at 63 parts per million with the regular fertilizer in the root application and the foliar application. The nanoprepared potassium was more readily taken up in the foliar application than a conventional potassium supplement in the foliar application (shown in the second bar  344 ). However, in both the root and foliar application, the formulation with nanoprepared potassium yielded a lower potassium concentration in the watermelons. 
     In contrast, the inclusion of PAMAM dendrimers with the nanoprepared potassium supplement in a foliar application in the fifth bar  350  shows an increase of approximately 7% over the root application of the regular fertilizer and conventional potassium supplement. The inclusion of the PAMAM dendrimers shows an increase of approximately a 12.6% increase relative to the same foliar application of the same formulation without the PAMAM dendrimers. The PAMAM dendrimers included in the formulation increase the transport of the potassium in the foliar application. 
       FIG. 6  and  FIG. 7  illustrate the additional benefit of the PAMAM dendrimers providing nitrogen and acting as a nitrogen supplement independently of the formulation in which the dendrimers are included.  FIG. 6  is a graph  452  showing the nitrogen concentration within millet plant tissue after a single application of dendrimers. 
     The first bar  454 , second bar  456 , and third bar  458  reflect different concentration levels of the applied dendrimers. The first bar  454  is a 1 part per billion (ppb) concentration of the dendrimers in the total volume of the as-applied spray. The second bar  456  is a 2-ppb concentration of the dendrimers in the total volume of the as-applied spray. The third bar  458  is a 3-ppb concentration of the dendrimers in the total volume of the as-applied spray. The fourth bar  460  depicts the control plants that did not receive a PAMAM dendrimer application. The first bar  454  reflects a low concentration of dendrimers applied to the millet and shows an approximate increase in nitrogen concentration in the plant tissue of 10% over the control. The second bar  456  reflects a medium concentration of dendrimers applied to the millet and shows an approximate increase in nitrogen concentration in the plant tissue of 5% relative to the low concentration. 
     The third bar  458  represents the nitrogen concentration in the plant tissue after a single application of a high concentration of the PAMAM dendrimers. A single foliar application of a high concentration of PAMAM dendrimers yielded an approximate increase of 30% over the control. The high concentration yielded an approximate increase of 14% in nitrogen in the plant tissue over the medium concentration. 
       FIG. 7  is a graph  562  that illustrates growth increase in the dry weight of wheat after a single dendrimer application versus a control. The first bar  564 , second bar  566 , and third bar  568  show the dry weight of the wheat with a PAMAM dendrimer application, while the fourth bar  570  reflects a control plot of wheat without PAMAM dendrimer application. 
     The first bar  564  shows the dry weight of the wheat after a low concentration application of the PAMAM dendrimers. The low concentration yielded approximately a 3.7% increase in the dry weight over the control. The second bar  566  shows the dry weight of the wheat after a medium concentration of the PAMAM dendrimers, and it reflects an approximate 6.4% increase over the control dry weight. The third bar  568  shows the dry weight of the wheat after a medium concentration of the PAMAM dendrimers, and it reflects an approximate 7.8% increase over the control dry weight. 
       FIG. 6  and  FIG. 7  reflect the ability of the PAMAM dendrimers alone to provide nitrogen to the plant (increasing the nitrogen concentration as shown in  FIG. 6 ) and to improve the growth rate of the plant (increasing the dry weight as shown in  FIG. 7 ). Dendrimers are conventionally used pharmaceutical applications to increase drug delivery. The use of PAMAM dendrimers in a fertilizer formulation unexpectedly provides an additional nitrogen supplement to the plants, increasing both the nitrogen concentration and the growth rate. In some embodiments, the nitrogen provided by the PAMAM dendrimers may further increase the effectiveness of the other active ingredient(s) in the fertilizer formulation, as well. 
     A fertilizer formulation including PAMAM dendrimers has been found to benefit from the inclusion of PAMAM dendrimers, but also may saturate above a particular concentration of the PAMAM dendrimers. The performance of the formulation is related the environment and the plants to which the formulation will be applied. In some embodiments, the mass to volume ratio of the dendrimers to the volume of fertilizer is in a range having an upper value, a lower value, or upper and lower values including any of 1 ppm, 2 ppm, 3 ppm, 4 ppm, 5 ppm, 6 ppm, 7 ppm, 8 ppm, 9 ppm, 10 ppm, or any values therebetween. For example, the mass to volume ratio may be greater than 1 ppm of dendrimers to fertilizer. In other examples, the mass to volume ratio may be less than 10 ppm. In yet other examples, the mass to volume ratio may be between 1 ppm and 10 ppm. In further examples, the mass to volume ratio may be between 3 ppm and 8 ppm. In at least one example, the mass to volume ratio may be about 6 ppm of PAMAM dendrimers to fertilizer. In a specific example, 37 mg of the PAMAM dendrimers is added to 4 ounces of a fertilizer and applied in an aqueous solution to an acre of plants. 
     In some cases, the ratio of dendrimers used in the formulation may be better characterized by the amount of dendrimers included in the total volume of the fertilizer formulation (including fertilizer and a liquid medium, such as water), as prepared. In some embodiments, the amount of dendrimers in the total volume of the formulation may be in a range having an upper value, a lower value, or upper and lower values including any of 1 part per billion (ppb), 2 ppb, 3 ppb, 4 ppb, 5 ppb, 6 ppb, 7 ppb, 8 ppb, 9 ppb, 10 ppb, or any values therebetween. For example, the amount of PAMAM dendrimers added to a fertilizer formulation may be greater than 1 ppb of the total volume of the formulation. In other examples, the amount of PAMAM dendrimers added to a fertilizer formulation may be less than 10 ppb of the total volume of the formulation. In yet other examples, the amount of PAMAM dendrimers added to a fertilizer formulation may be between 1 ppb and 10 ppb of the total volume of the formulation. In further examples, the amount of PAMAM dendrimers added to a fertilizer formulation may be between 3 ppb and 8 ppb of the total volume of the formulation. In at least one example, the amount of PAMAM dendrimers added to a fertilizer formulation may be about 6 ppb of the total volume of the formulation. In a particular example, a 15-gallon aqueous fertilizer formulation containing 100 milliliters of fertilizer may have 4 micrograms of PAMAM dendrimers added. In other examples, a formulation for one acre may have about 15 micrograms of PAMAM dendrimers added. In yet other examples, a formulation for one acre may have about 30 micrograms of PAMAM dendrimers added. In further examples, a formulation for one acre may have less than 37 micrograms of PAMAM dendrimers added. 
     In some examples, it may be crucial that the amount of PAMAM dendrimers added does not exceed 10 ppb of the total formulation. In some formulations, exceeding 10 ppb concentration of the dendrimers in the total volume of the formulation may increase aggregation of the dendrimers with one another, reducing total amount of available dendrimers to interact with the fertilizer and to increase the transport mobility of the fertilizer during application. 
     Some formulations of fertilizer and a liquid medium may have a volume ratio of 1:160, such as a fertilizer formulation containing 4 ounces of fertilizer and 5 gallons of water that is applied from a spray tank. Other formulations of fertilizer and a liquid medium may have a volume ratio of 1:32000; such as a fertilizer formulation containing 4 ounces of fertilizer and 1000 gallons of water that is applied through a general irrigation system. In some embodiments, a formulation may include a volume ratio of fertilizer to a liquid medium in a range having an upper value, a lower value, or upper and lower values including any of 1:160, 1:240, 1:400, 1:800, 1:1600, 1:3200, 1:6400, 1:16000, 1:32000, or any values therebetween. For example, fertilizer formulations including PAMAM dendrimers may have a volume ratio of the fertilizer to the liquid medium less than 1:160. In other examples, the fertilizer formulations including PAMAM dendrimers may have a volume ratio of the fertilizer to the liquid medium greater than 1:32000. In yet other examples, the fertilizer formulations including PAMAM dendrimers may have a volume ratio of the fertilizer to the liquid medium between 1:160 and 1:32000. In at least one example, the fertilizer formulations including PAMAM dendrimers may have a volume ratio of the fertilizer to the liquid medium of about 1:3200. 
     As described herein, the formulation may have different characteristics based on the needs of different plants. For example, the acidity of the formulation may change to tailor the formulation to the application. In some embodiments, the formulation containing PAMAM dendrimers has a pH less than 8.0 In other embodiments, the formulation containing PAMAM dendrimers has a pH less than 7.0 (i.e., more acidic than neutral). In yet other embodiments, the formulation has a pH less than 6.5. A formulation with a pH less than 6.5 may allow the PAMAM dendrimers to interact with the active fertilizer ingredient in the formulation more readily and to more efficiently increase the transport rate of the active ingredient. 
     One or more specific implementations of the present disclosure are described herein. These described implementations are examples of the presently disclosed techniques. Additionally, in an effort to provide a concise description of these implementations, not all features of an actual implementation may be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions will be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. 
     The articles “a,” “an,” and “the” are intended to mean that there are one or more of the elements in the preceding descriptions. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Additionally, it should be understood that references to “one implementation” or “an implementation” of the present disclosure are not intended to be interpreted as excluding the existence of additional implementations that also incorporate the recited features. For example, any element described in relation to an implementation herein may be combinable with any element of any other implementation described herein. Numbers, percentages, ratios, or other values stated herein are intended to include that value, and also other values that are “about” or “approximately” the stated value, as would be appreciated by one of ordinary skill in the art encompassed by implementations of the present disclosure. A stated value should therefore be interpreted broadly enough to encompass values that are at least close enough to the stated value to perform a desired function or achieve a desired result. The stated values include at least the variation to be expected in a suitable manufacturing or production process, and may include values that are within 5%, within 1%, within 0.1%, or within 0.01% of a stated value. 
     A person having ordinary skill in the art should realize in view of the present disclosure that equivalent constructions do not depart from the spirit and scope of the present disclosure, and that various changes, substitutions, and alterations may be made to implementations disclosed herein without departing from the spirit and scope of the present disclosure. Equivalent constructions, including functional “means-plus-function” clauses are intended to cover the structures described herein as performing the recited function, including both structural equivalents that operate in the same manner, and equivalent structures that provide the same function. It is the express intention of the applicant not to invoke means-plus-function or other functional claiming for any claim except for those in which the words ‘means for’ appear together with an associated function. Each addition, deletion, and modification to the implementations that falls within the meaning and scope of the claims is to be embraced by the claims. 
     The terms “approximately,” “about,” and “substantially” as used herein represent an amount close to the stated amount that still performs a desired function or achieves a desired result. For example, the terms “approximately,” “about,” and “substantially” may refer to an amount that is within less than 5% of, within less than 1% of, within less than 0.1% of, and within less than 0.01% of a stated amount. Further, it should be understood that any directions or reference frames in the preceding description are merely relative directions or movements. For example, any references to “up” and “down” or “above” or “below” are merely descriptive of the relative position or movement of the related elements. 
     The present disclosure may be embodied in other specific forms without departing from its spirit or characteristics. The described implementations are to be considered as illustrative and not restrictive. The scope of the disclosure is, therefore, indicated by the appended claims rather than by the foregoing description. Changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope.