In this study, several simple equations are suggested to investigate the effects of size and density on the number, surface area, stiffening efficiency, and specific surface area of nanoparticles in polymer nanocomposites. In addition, the roles of nanoparticle size and interphase thickness in the interfacial/interphase properties and tensile strength of nanocomposites are explained by various equations. The aggregates/agglomerates of nanoparticles are also assumed as large particles in nanocomposites, and their influences on the nanoparticle characteristics, interface/interphase properties, and tensile strength are discussed. The small size advantageously affects the number, surface area, stiffening efficiency, and specific surface area of nanoparticles. Only 2 g of isolated and well-dispersed nanoparticles with radius of 10 nm (R = 10 nm) and density of 2 g/cm3 produce the significant interfacial area of 250 m2 with polymer matrix. Moreover, only a thick interphase cannot produce high interfacial/interphase parameters and significant mechanical properties in nanocomposites because the filler size and aggregates/agglomerates also control these terms. It is found that a thick interphase (t = 25 nm) surrounding the big nanoparticles (R = 50 nm) only improves the B interphase parameter to about 4, while B = 13 is obtained by the smallest nanoparticles and the thickest interphase.
Paratuberculosis, or Johne's disease, is a chronic, granulomatous, gastrointestinal tract disease of cattle and other ruminants caused by the bacterium Mycobacterium avium, subspecies paratuberculosis (MAP). Control of Johne's disease is based on programs of testing and culling animals positive for infection with MAP while concurrently modifying management to reduce the likelihood of infection. The current study is motivated by the hypothesis that genetic variation in host susceptibility to MAP infection can be dissected and quantifiable associations with genetic markers identified. For this purpose, a case-control, genome-wide association study was conducted using US Holstein cattle phenotyped for MAP infection using a serum ELISA and/or fecal culture test. Cases included cows positive for either serum ELISA, fecal culture or both. Controls consisted of animals negative for the serum ELISA test or both serum ELISA and fecal culture when both were available. Controls were matched by herd and proximal birth date with cases. A total of 856 cows (451 cases and 405 controls) were used in initial discovery analyses, and an additional 263 cows (159 cases and 104 controls) from the same herds were used as a validation data set. Data were analyzed in a single marker analysis controlling for relatedness of individuals (GRAMMAR-GC) and also in a Bayesian analysis in which multiple marker effects were estimated simultaneously (GenSel). For the latter, effects of non-overlapping 1 Mb marker windows across the genome were estimated. Results from the two discovery analyses were generally concordant; however, discovery results were generally not well supported in analysis of the validation data set. A combined analysis of discovery and validation data sets provided strongest support for SNPs and 1 Mb windows on chromosomes 1, 2, 6, 7, 17 and 29.