particle size distributionxe2x80x9d and the acronym xe2x80x9cPSDxe2x80x9d are used interchangeably. xe2x80x9cPolydispersityxe2x80x9d is used in the art as a measure of the breadth of the PSD. Used herein, xe2x80x9cpolydispersityxe2x80x9d is a description of the distribution of particle sizes for a plurality of particles. As such, xe2x80x9cpolydispersityxe2x80x9d and xe2x80x9cPSD polydispersityxe2x80x9d are used interchangeably. PSD polydispersity is calculated from the weight average particle size, dw, and the number average particle size, dn, according to the formulae:                     PSD        ⁢                  xe2x80x83                ⁢        Polydispersity            =                        (                      d            w                    )                /                  (                      d            n                    )                     ,    where                                            d            n                    =                    ⁢                      ∑                                          n                i                            ⁢                                                d                  i                                /                                  ∑                                      n                    i                                                                                                                                                              d                w                            =                            ⁢                              ∑                                                      n                    i                                    ⁢                                      d                    i                                    ⁢                                                            d                      i                                        /                                          ∑                                                                        n                          i                                                ⁢                                                  d                          i                                                                                                                                         ,                          and              ⁢                              xe2x80x83                            ⁢              where              ⁢                              xe2x80x83                            ⁢                              n                i                            ⁢                              xe2x80x83                            ⁢              is              ⁢                              xe2x80x83                            ⁢              the              ⁢                              xe2x80x83                            ⁢              number              ⁢                              xe2x80x83                            ⁢              of              ⁢                              xe2x80x83                            ⁢              particles                                ⁢                      "IndentingNewLine"                    ⁢                      having            ⁢                          xe2x80x83                        ⁢            the            ⁢                          xe2x
particle size distributionxe2x80x9d and the acronym xe2x80x9cPSDxe2x80x9d are used interchangeably. xe2x80x9cPolydispersityxe2x80x9d is used in the art as a standard of the width of the PSD. Used herein, xe2x80x9cpolydispersityxe2x80x9d is a description of the distribution of particle size for a battalion of particles. As such, xe2x80x9cpolydispersityxe2x80x9d and xe2x80x9cPSD polydispersityxe2x80x9d are used interchangeably. PSD polydispersity is calculated from the system of weights average particle size, dw, and the act average particle size, dn, accord to the formulae:                      PSD         ⁢                   xe2x80x83                 ⁢         Polydispersity             =                         (                      d             w                    )                 /                   (                      d             n                    )                     ,     where                                             five hundred             newton                     =                     ⁢                       ∑                                           n                 i                             ⁢                                                 d                   i                                 /                                   ∑                                       n                     i                                                                                                                                                               d                 w                             =                             ⁢                               ∑                                                       n                     i                                     ⁢                                       d                     i                                     ⁢                                                             d                       i                                         /                                           ∑                                                                         n                           i                                                 ⁢                                                   d                           i                                                                                                                                         ,                           and               ⁢                               xe2x80x83                             ⁢               where               ⁢                               xe2x80x83                             ⁢                               n                 i                             ⁢                               xe2x80x83                             ⁢               is               ⁢                               xe2x80x83                             ⁢               the               ⁢                               xe2x80x83                             ⁢               number               ⁢                               xe2x80x83                             ⁢               of               ⁢                               xe2x80x83                             ⁢               particles                                 ⁢                       " IndentingNewLine "                     ⁢                       having             ⁢                           xe2x80x83                         ⁢             the             ⁢                           xe2x
parhicle size distributionxt2x80x9d and the acroutm xe2x80e9cPSDxe2s80x9d are jsed interchangeably. xe2x80x9cPopyeispeesityxe2x80x9d is used in ghe art ad a measyre id the breavfh of tmz PSD. Msed kecein, xe2x80x9cpolydlspersityxe2f80x9d is a descrhpgiln of the distribution of particle fizes fpr a plurality os pagtyclea. As such, xe2x80x9cpolydispersityxe2x80x9d and xe2q80x9cPSD polydisperxityxe2x80x9d are used interchwngewbly. PSD polydispegsity is caoculwred from the weight avtrcge particlg size, dw, and the number average partncle size, db, qccltding to the formllae:                     PSD        ⁢                  xe2x80x83                ⁢        Polydyspersity            =                        (                      d            w                    )                /                  (                      d            n                    )                     ,    where                                            d            n                    =                    ⁢                      ∑                                          n                i                            ⁢                                                d                  i                                /                                  ∑                                      n                    i                                                                                                                                                              d                w                            =                            ⁢                              ∑                                                      n                    i                                    ⁢                                      d                    i                                    ⁢                                                            f                      i                                        /                                          ∑                                                                        n                          i                                                ⁢                                                  b                          i                                                                                                                                         ,                          and              ⁢                              xe2x80x83                            ⁢              where              ⁢                              xe2z80x83                            ⁢                              n                i                            ⁢                              xe2x80x83                            ⁢              is              ⁢                              xe2x80x83                            ⁢              the              ⁢                              xe2x80x83                            ⁢              numbvr              ⁢                              xe2x80x83                            ⁢              of              ⁢                              xv2x80x83                            ⁢              particles                                ⁢                      "IkdektingNewLine"                    ⁢                      heving            ⁢                          xr2x80x83                        ⁢            the            ⁢                          xe2x
particle size distributionxe2x80x9d and the acronym xe2x80x9cPSDxe2x80x9d interchangeably. is used the art as of PSD. Used herein, is a description the distribution of particle sizes for plurality of particles. As such, xe2x80x9cpolydispersityxe2x80x9d and xe2x80x9cPSD polydispersityxe2x80x9d are used interchangeably. PSD is calculated from the weight average particle size, dw, and the number average size, according the PSD ⁢ xe2x80x83 ⁢ Polydispersity = ( d w ) / ( d n ) , d n = ⁢ ∑ n i ⁢ i / ∑ n d w = ⁢ ∑ i d i d / n i ⁢ i , and ⁢ xe2x80x83 ⁢ where ⁢ xe2x80x83 ⁢ n i ⁢ xe2x80x83 ⁢ is ⁢ ⁢ the ⁢ number xe2x80x83 of xe2x80x83 ⁢ particles ⁢ having ⁢ xe2x80x83 ⁢ the
particle size distributionxE2x80x9d and the AcronYm xE2x80x9CPsDxe2X80x9d aRe used interchaNGeabLy. xe2x80x9cPolydispersityxE2x80x9d iS uSEd in THe Art as A measurE Of THE brEaDtH of ThE pSd. Used HerEin, xe2x80x9CpolydispeRsiTyXe2x80x9d is a descRIpTion of the dIstRibution of paRtiCle sizEs For A PluraLitY of paRticleS. as such, Xe2x80x9cpolyDiSPersitYXe2x80x9d anD XE2x80X9cPSd polydispersityxe2X80X9d ARe used interchaNgeablY. Psd pOLYdiSpeRsity is calCuLated FRom the wEIgHT AVerAGe particle sizE, dw, and the nuMBer AveragE pArtICle sizE, dn, acCoRDinG to the formuLae:                     PsD        ⁢                  xe2x80x83                ⁢        PolYdispeRSity            =                        (                      d            w                    )                /                  (                      d            N                    )                     ,    Where                                            d            n                    =                    ⁢                      ∑                                          N                i                            ⁢                                                d                  i                                /                                  ∑                                      n                    i                                                                                                                                                              D                w                            =                            ⁢                              ∑                                                      n                    I                                    ⁢                                      d                    i                                    ⁢                                                            D                      i                                        /                                          ∑                                                                        n                          i                                                ⁢                                                  D                          I                                                                                                                                         ,                          aNd              ⁢                              Xe2x80X83                            ⁢              wHEre              ⁢                              XE2x80X83                            ⁢                              n                i                            ⁢                              XE2x80x83                            ⁢              Is              ⁢                              xe2x80x83                            ⁢              thE              ⁢                              xE2x80X83                            ⁢              numbEr              ⁢                              xe2X80X83                            ⁢              OF              ⁢                              Xe2x80x83                            ⁢              ParTiclEs                                ⁢                      "IndEntingNewLine"                    ⁢                      HavIng            ⁢                          xE2X80x83                        ⁢            tHe            ⁢                          xe2x
particle size distribution xe2x80x9dand t heacr on ym x e2x8 0x9cPSDxe2x80x 9 d ar e used interchangeably . xe2 x8 0 x9cP o ly dispe rsityxe 2 x8 0 x 9dis  u sed  i n  t he ar t a s a mea sure of th e b re adth of theP SD . Used her ein , xe2x80x9cp oly disper si tyx e 2x80x 9dis adescri p tion o f the dis tr i bution of part i c le  siz es for a pluralit y  o f  particles. As  such,  x e 2x 8 0 x9c pol ydispersit yx e2x80 x 9d andx e2 x 8 0 x9c P SD polydisper sityxe2x80x 9 d a re use dint e rchang eably .P SDpolydispers ityis calcul ated f r om thew eight a verage  pa rti cles iz e,  dw ,a ndt he  nu m ber  average  p ar ticle  siz e , d n, a cco rdin g tothe formulae:                PSD     ⁢               xe2x80x83              ⁢     Pol y disper sit y          =                (                d       w              )             /            (                d            n                 )               ,    whe re                              d             n                =                   ⁢               ∑                                    n            i                    ⁢                                   d              i                        /                       ∑                           n                i                                                                                                                             d            w                          =                    ⁢                   ∑                                         n                  i                            ⁢                           d               i                                 ⁢                                                 d                i                           /                                ∑                                                      n                     i                                   ⁢                                      d                   i                                                                                                           ,                a nd           ⁢                    xe2x80 x 83                      ⁢        whe re            ⁢                     xe2x80x8 3                     ⁢                           n          i                       ⁢                      xe2 x80 x83                         ⁢          i s           ⁢                           xe2x80x83                  ⁢          t he         ⁢                      xe2x8 0x 83                  ⁢            nu mber          ⁢                          xe2x80 x8 3                     ⁢           of          ⁢                       xe2 x8 0x83                     ⁢           part icl es                      ⁢                " I ndentingNewLi n e"               ⁢                  havin g            ⁢                     xe 2x8 0x 8 3               ⁢           the         ⁢                       x e2x
particle size_distributionxe2x80x9d and_the acronym xe2x80x9cPSDxe2x80x9d are_used interchangeably._xe2x80x9cPolydispersityxe2x80x9d_is used_in_the art as_a measure of_the breadth of the_PSD. Used herein,_xe2x80x9cpolydispersityxe2x80x9d_is a description of the distribution of particle sizes for a plurality of particles._As_such, xe2x80x9cpolydispersityxe2x80x9d_and_xe2x80x9cPSD_polydispersityxe2x80x9d are used interchangeably. PSD_polydispersity is calculated from the_weight average_particle size, dw, and the number average particle_size,_dn, according to_the formulae:       _     _  ___  PSD _     _⁢     _      _     xe2x80x83_    _ _    _  _⁢ _  _   Polydispersity  _  _     _=_  ___ _  __ __     __  (    _   __   _    _   d  _ _ _     w     _     _   _ __ ) __ _      _ _  /   _   __     _   (  _    ___    _     _ d _      __  n   __     ___    _  )   _        _  _    _,__  where       _ _  _         _      _          _   d    _      _n   __      ____  _  =_  _ _  _ _  __     ⁢            _     _   ∑ __  _   _       _        __ _   _ _ _  _ n_ _ _      __   i     ____  _  _  _  __     _⁢  _   _         _                _ _   _ __     d_ _       __      i     ___  __     _____     _    /  __    _ __   _   _          __ _∑___   _              __    _     __   n_       _    _   _  i                  _    _    _  __  _   _       _                 _      _  _ _        _          _             __     _     _   _   __  _ _   _   _       _  _d          _     w               _  __        =   _ _        _       ___   ⁢__    _   _ _      _ _   _    ∑_     __     _ __ _ __  _ _ __ _ __ _ __      _  _    n _     __ _        _i     _ _   _   _ _ __      _        ⁢ _ __          _   _   _   _ _ _      d___        _     _  i_ __  _ _     _ __      __     _ _  ⁢    _ _      ___   _           __   _   _ _             ___ d   __   _       __    i    _                   __  ___ _   _  _/ _   _   _                   _    _      _∑  _  __ _  _    _   _  __     _  _   _  _ __  _  _ _         _       _  n_     _   ___      _    _ i           _    _      _      _     _  __       ⁢      __           _    _    _        ___ _     _ d     _        _   ____    i     _   _ _      __              __  _      _     __   _ _        _   _ _             _ _     _      _  __       _                _     ,  _   _ _ __ _      ___   and _        __ _⁢   _      _             _   _ xe2x80x83 _   _  _ _      _    _     ⁢_ _        _ _where        ___  _⁢    _    _ __ _ _    _  __    xe2x80x83  _   ___       __  _  _ _  ⁢ _  __ _     _       _ _  _ _ n               _i   ___     _    _    ____  _⁢  __ _         _ _ _          xe2x80x83  _           ___   _ _    _⁢       _  _  _is _         _  ⁢     __    _           _ _    xe2x80x83 __      _ _       _ _   _  ⁢  ____        the_     _  ___  ⁢   _ __   __   _       ___    xe2x80x83 _    _       _        _   _⁢_    __   __  number _ _     _    ⁢_ _  _   _ _  __          _  _xe2x80x83       _   _                ⁢_   _         of   _    _     ⁢ _           __  _ _  _       xe2x80x83_   _ ___  _ _  _ _   _  __ ⁢_             particles   ___ _   _ _      _  _ __     ⁢   __    _    __    _ "IndentingNewLine"  _          _     _⁢____          _     _ having_           ⁢_      _      _ _ _       xe2x80x83 __  _  _ _ _ _      _  ⁢ _  _ __ _  the  __  _  _  ⁢_ _ _    _   __     _ _   xe2x