Assessing depletion attractions between colloidal nanocrystals Wiley VCH 04/11/2025 10587814 10.1126/sciadv.adv2216 Science Advances 2375-2548 11 15 Charles K OfosuTanner A WilcoxsonTsung-Lun LeeWilliam D BrackettJinny ChoiThomas M TruskettDelia J Milliron Adding nonadsorbing polymers to hard microsphere dispersions generates osmotic depletion attractions that can be quantitatively predicted and designed to manipulate colloidal phase behavior. Whether depletion described by classical theories is the mechanism for polymer-mediated nanosphere attractions is less evident. Colloidal hard nanospheres and nonadsorbing polymers are challenging to realize given the diverse interactions typically present in nanoparticle dispersions. Here, we use small-angle x-ray scattering to assess whether the depletion mechanism holds at the nanoscale, leveraging a recent finding that uncharged, oleate-capped indium oxide nanocrystals exhibit near–hard-sphere interactions in toluene. Classical modeling of polystyrene depletant as penetrable spheres predicts depletion-induced phase boundaries, nanocrystal second osmotic virial coefficients, and colloidal structuring in agreement with experiments for polymer radii of gyration up to 80% of the nanocrystal radius. Experimentally observed weakening of depletion interactions for larger polymer-to-nanocrystal size ratios qualitatively follows theoretical predictions that account for how polymer physics influences depletant interactions.

]]>

] khm f v hsg q] c ht r n e f x q] shn m 'h-d -) P C = P e ≈ . 5 2 ( '3 6 ( n m kx en q b g ] hm r n e l n kd b t k] q v d hf g s 0 u 1 1 0 5 '1 / 1 4 ( 8 @ o qhk 1 / 1 1 1 0 5 '1 / 1 4 ( 8 @ o qhk 1 / 1

n e 0 /

3 -S -A -L Z qshm *S -D -H-F Z qsm d q* Q -K -In m d r* B -Q -R m x c d q* @ -IZ x Z qZ l Z m * o x O Q HR L 9 @b n l o t sZ shn m Z k sn n k en q khp t hc ,rsZ sd sg d n qx b Z kb t kZ shn m r n e l Z b qn l n kd b t kZ q l Z sd qhZ kr-L U a qn l n kd a t kd r 4 0 * 1 8 / 5 z 1 8 1 1 '1 / 0

(-6 4 -I-@ -@ m c d qrn m * I-F kZ rd q* R -B -F kn sy d q* G N N L C ,a kt d 9 @ o x sg n m o Z b j Z f d en q g hf g , o d qen ql Z m b d l n kd b t kZ q c x m Z l hb r Z m c g Z qc o Z qshb kd L n m sd B Z qkn rhl t kZ shn m r-B n l o , L U sd q,R a h, 0 6 2 * 0 /

2 5 2 '1 / 1 / (-6 5 -U -Q Z l Z rt a qZ l Z m h* A -C -C hb d * D -R -G Z qo d q* L -O-R o d kkhm f r* I-@ -@ m c d qrn m * R -B -F kn sy d q* eqd t c

@ rn esv Z qd rt hsd en q g hf g sg qn t f g o t s Z m Z kx rhr n e o Z qshb kd rhl t kZ shn m c Z sZ -B n l o t s, N g w r,B n l l t m , 1 4 3 * 0 / 6 1 6 4 '1 / 1 / (-6 6 -C -G d x d r* I-L d kqn rd * A qn v m hZ m c x m Z l hb r rhl t kZ shn m r n e l n c d k g Z qc ,ro g d qd rt ro d m rhn m r-I,M n m m d v sn m ,E kt hc L d a g , 3 5 * 0 z 1 7 '0 8 8 2 (-6 7 -I-E n w * F -S g n l Z r* O-I-E kn qx * R d b n m c ,n qc d q sqZ m rhshn m sd l o d qZ st qd r Z m c qd kZ sd c o qn o d qshd r n e o n kx rsx qd m d -H-Hm fl t d m b d n e l n kd b t kZ q v d hf g s-I,: o o k,N g w r, 1 0 * 4 7 0 z 4 8 0 '0 8 4 / (-6 8 -K -I-E d ssd qr* M -G Z c ihb g qhrshc hr* I-R -K hm c m d q* I-V -L Z x r* L n kd b t kZ q v d hf g s c d o d m c d m b d n e g x c qn c x m Z l hb Z m c sg d ql n c x m Z l hb o qn o d qshd r en q v d kk,c d fi m d c khm d Z q o n kx l d qr hm rn kt shn m -I,N g w r,B g d l ,P d e,C U sU L n m n f q, 1 2 * 5 0 8 z 5 3 / '0 8 8 3 (-7 / -J -S d qZ n * A -R -E Z ql d q*X -M Z j Z l t qZ * G -HZ sqn t * J -G n m f * I-V -L Z x r* Q Z c ht r n e f x qZ shn m n e o n kx rsx qd m d b n l a r Z m c b d m sho d c d r hm Z = rn ku d m s-L U a qn l n kd a t kd r 2 7 * 0 3 3 6 z 0 3 4 / '1 / / 4 (-